22. Q22a
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Similar Question 1
<p>Explain how you know that the origin is the centre of the circle defined by the equation <code class='latex inline'>x^2 + y^2 = 45</code>.</p>
Similar Question 2
<ul> <li>State the coordinates of the centre of the circle described by each equation below.</li> <li>State the radius and the x— and y—intercepts of the circle.</li> <li>Sketch a graph of the circle.</li> </ul> <p><code class='latex inline'> \displaystyle x^2 + y^2 = 2.89 </code></p>
Similar Question 3
<p>Chanelle is creating a design for vinyl flooring. She uses circles and squares to create the design, as shown. If the equation of the small circle is <code class='latex inline'>x^2+y^2=16</code>, what are the dimensions of the large square?</p><img src="/qimages/716" />
Similar Questions
Learning Path
L1 Quick Intro to Factoring Trinomial with Leading a
L2 Introduction to Factoring ax^2+bx+c
L3 Factoring ax^2+bx+c, ex1
Now You Try
<p>For each equation of a circle:</p><p><strong>i)</strong> Determine the radius.</p><p><strong>ii)</strong> State the x- and y-intercepts.</p><p> <code class='latex inline'>x^2+y^2=49</code></p>
<p>Which of the following could be a list the points that satisfy each condition and have integer coordinates: 5 units from the origin.</p>
<p>Is the following points are on the circle with equation <code class='latex inline'>x^2+y^2=65</code>? Explain.</p><p><code class='latex inline'>(-4,7)</code></p>
<p>Find the radius of the circle represented by the equation <code class='latex inline'>kx^2 + ky^2 = r^2</code>, where <code class='latex inline'>k > 0</code>.</p>
<p>a) Determine the coordinates of the other endpoint of the diameter shown.</p><img src="/qimages/5180" /><p>b) does any other point on the circle have an x-coordinate of 3? </p><p>c) Determine the equation for the circle.</p><p>d) Show that the point you found in part a) can be verified using the equation in part c)</p>
<p>A satellite orbits Earth on a path with <code class='latex inline'>x^2+y^2=45000000</code>. Another satellite, in the same plane, is currently located at <code class='latex inline'>(12504,16050)</code>. Is the satellite in or outside the first orbit.</p>
<p> Determine an equation for each circle.</p><img src="/qimages/625" />
<p>State the domain and range of each relation.</p><img src="/qimages/584" />
<p>Points <code class='latex inline'>P(-9,2)</code> and <code class='latex inline'>Q(9,-2)</code> are endpoints of a diameter of a circle.</p><p>Write the equation of the circle.</p>
<p>Verify that the points <code class='latex inline'>R(-3, 6)</code> and <code class='latex inline'>S(-6, -3)</code> lie on the circle <code class='latex inline'>x^2 + y^2 = 45</code>.</p>
<p>Find the centre of the circle that passes through the points <code class='latex inline'>A(-7, 4), B(-4. 5)</code>, and <code class='latex inline'>C(0, 3)</code>.</p>
<p>Verify that <code class='latex inline'>OM</code> is perpendicular to <code class='latex inline'>AB</code>.</p><img src="/qimages/746" />
<p>Points <code class='latex inline'>P(-9,2)</code> and <code class='latex inline'>Q(9,-2)</code> are endpoints of a diameter of a circle.</p><p><code class='latex inline'>\angle PRQ</code> is </p>
<p>Describe the region defined by each inequality. Then. draw and label a diagram of the three regions.</p><p> <code class='latex inline'>x^2 + y^2 > 49</code></p>
<p>A truck with a wide load, proceeding slowly along a secondary road, is approaching a tunnel that is shaped like a semicircle. The maximum height of the tunnel is <code class='latex inline'>5.25</code> m. If the load is 8 m wide and <code class='latex inline'>3.5</code> m high, will it fit through the tunnel? </p><p>What is the diagonal length from bottom middle of the load to the edge of the load?</p>
<p>Use the given information to write an equation for a circle with centre <code class='latex inline'>(0,0)</code>.</p> <ul> <li>radius of 11 units</li> </ul>
<p>Use the given information to write an equation for a circle with centre <code class='latex inline'>(0,0)</code>.</p> <ul> <li> x-intercepts <code class='latex inline'>(-9,0)</code> and <code class='latex inline'>(9,0)</code></li> </ul>
<p> Determine an equation for each circle.</p><img src="/qimages/623" />
<p> Determine an equation for each circle.</p><img src="/qimages/624" />
<p>An equation for the small circle in this design is <code class='latex inline'>x^2 + y^2 = 4</code>.</p><p>Determine an equation for the larger circle.</p><img src="/qimages/632" />
<p>Is the following points are on the circle with equation <code class='latex inline'>x^2+y^2=65</code>? Explain.</p><p><code class='latex inline'>(5,-6)</code></p>
<p>Write the equation of a circle with centre <code class='latex inline'>(0,0)</code> and radius <code class='latex inline'>r</code>.</p><p><code class='latex inline'>r=2\displaystyle{\frac{1}{3}}</code></p>
<p> Find the slope of the chord <code class='latex inline'>AB</code>.</p><img src="/qimages/746" />
<p>Chanelle is creating a design for vinyl flooring. She uses circles and squares to create the design, as shown. If the equation of the small circle is <code class='latex inline'>x^2+y^2=16</code>, what are the dimensions of the large square?</p><img src="/qimages/716" />
<p>Circle that is centred at <code class='latex inline'>(0,0)</code> and passes through</p> <ul> <li>i) <code class='latex inline'>(-3,4)</code></li> <li>ii) <code class='latex inline'>(5,0)</code></li> <li>iii) <code class='latex inline'>(0,-3)</code></li> <li><p>iv) <code class='latex inline'>(8,-15)</code></p></li> <li><p>Which of the following coordinates represent two other points on each circle for each circle above.</p></li> </ul>
<p>Determine the midpoint coordinates and the length of each line segment.</p><img src="/qimages/5606" />
<p>For each equation of a circle:</p><p><strong>i)</strong> Determine the radius.</p><p><strong>ii)</strong> State the x- and y-intercepts.</p><p> <code class='latex inline'>x^2+y^2=36</code></p>
<p>Use the given information to write an equation for a circle with centre <code class='latex inline'>(0,0)</code>.</p> <ul> <li>diameter of 12 units</li> </ul>
<p>Use the given information to write an equation for a circle with centre <code class='latex inline'>(0,0)</code>.</p> <ul> <li>y-intercepts <code class='latex inline'>(0,-4)</code> and <code class='latex inline'>(0,4)</code></li> </ul>
<p>Determine the equation of a circle that has a diameter with endpoints <code class='latex inline'>(-8,15)</code> and <code class='latex inline'>(8,-15)</code>.</p>
<p>A ship drops its anchor into the water and creates a circular ripple. The radius of this ripple increases at a rate of <code class='latex inline'>50 cm/s</code>.</p> <ul> <li><p>(a) Find an equation for the circle 10 s after the anchor is dropped.</p></li> <li><p>(b) A small rowboat is <code class='latex inline'>50 m</code> east and <code class='latex inline'>75 m</code> north of the point where the anchor was dropped. How long does the ripple take to reach the rowboat?</p></li> </ul> <p>Describe any assumptions you made for your answers to parts a) and b).</p>
<p>Write the equation of a circle with centre <code class='latex inline'>(0,0)</code> and radius <code class='latex inline'>r</code>.</p><p><code class='latex inline'>r=0.25</code></p>
<p>For each equation of a circle:</p><p><strong>i)</strong> Determine the radius.</p><p><strong>ii)</strong> State the x- and y-intercepts.</p><p><code class='latex inline'>x^2+y^2=169</code></p>
<p>Describe the circle with each equation.</p><p> <code class='latex inline'>(x-2)^2+(y+4)^2=9</code></p>
<p>Points <code class='latex inline'>(a,5)</code> and <code class='latex inline'>(9, b)</code> are on the circle <code class='latex inline'>x^2+y^2=125</code>. Determine the possible values of <code class='latex inline'>a</code> and <code class='latex inline'>b</code>. Round to one decimal place, if necessary. </p>
<p>A circle that is centred at <code class='latex inline'>(0,0)</code> and passes through</p><p>i) <code class='latex inline'>(-3,4)</code></p><p>ii) <code class='latex inline'>(5,0)</code></p><p>iii) <code class='latex inline'>(0,-3)</code></p><p>iv) <code class='latex inline'>(8,-15)</code></p> <ul> <li> Write the equation of each circle above.</li> </ul>
<p>Explain how you know that the origin is the centre of the circle defined by the equation <code class='latex inline'>x^2 + y^2 = 45</code>.</p>
<p>Write the equation of a circle with centre <code class='latex inline'>(0,0)</code> and radius <code class='latex inline'>r</code>.</p><p><code class='latex inline'>r=3</code></p>
<p>A relation is defined by <code class='latex inline'>x^2+y^2=36</code>.</p><p><strong>(a)</strong> Graph the relation.</p><p><strong>(b)</strong> State the domain and range of the relation.</p><p><strong>(c)</strong> Is the relation a function? Explain. </p>
<ul> <li>State the coordinates of the centre of the circle described by each equation below.</li> <li>State the radius and the x— and y—intercepts of the circle.</li> <li>Sketch a graph of the circle.</li> </ul> <p><code class='latex inline'> \displaystyle x^2 + y^2 = 2.89 </code></p>
<p>Verify that the centre of this circle lies on the right bisector of the chord <code class='latex inline'>PQ</code>.</p><img src="/qimages/747" /><p><strong>(a)</strong> Explain how you know that the origin is the centre of the circle defined by the equation <code class='latex inline'>x^2 + y^2 = 45</code>.</p><p><strong>(b)</strong> Verify that the points <code class='latex inline'>R(-3, 6)</code> and <code class='latex inline'>S(-6, -3)</code> lie on the circle.</p><p><strong>(c)</strong> Verify that the line through the origin and the midpoint of the chord <code class='latex inline'>RS</code> is perpendicular to the chord.</p>
<p>Plot points <code class='latex inline'>A, B</code>, and <code class='latex inline'>C</code> on grid paper, and draw the circle that passes through the points. Use your drawing to check your answers to parts a) and b).</p>
<p> Determine the radius of a circle that is centred at <code class='latex inline'>(0,0)</code> and passes through</p><p><strong>i)</strong> <code class='latex inline'>(-3,4)</code></p><p><strong>ii)</strong> <code class='latex inline'>(5,0)</code></p><p><strong>iii)</strong> <code class='latex inline'>(0,-3)</code></p><p><strong>iv)</strong> <code class='latex inline'>(8,-15)</code></p>
<p>Which of the following could be a list the points that satisfy each condition and have integer coordinates: <code class='latex inline'>10</code> units from the point <code class='latex inline'>(-5, -2)</code></p>
<p>Describe the region defined by each inequality. Then. draw and label a diagram of the three regions.</p><p> <code class='latex inline'>25 < x^2 + y^2 < 49</code></p>
<p><strong>(a)</strong> Verify that the points <code class='latex inline'>P(-1, -2), Q(2, 7)</code>, and <code class='latex inline'>R(6, 5)</code> are equidistant from the point <code class='latex inline'>C(2, 2)</code>.</p><p><strong>(b)</strong> Draw the circle that passes through points P, Q, and R.</p>
<p>Is the following points are on the circle with equation <code class='latex inline'>x^2+y^2=65</code>? Explain.</p><p><code class='latex inline'>(-3,-6)</code></p>
<p>Which of the following could be a list the points that satisfy each condition and have integer coordinates: <code class='latex inline'>5</code> units from the point <code class='latex inline'>(2, 1)</code></p>
<p><strong>a)</strong> Draw the triangle with vertices <code class='latex inline'>Q(-2, 0)</code>, <code class='latex inline'>R(2, 8)</code>, and <code class='latex inline'>S(7, 3)</code>. Then, construct the right bisector of each side.</p><p><strong>b)</strong> Verify algebraically that the three right bisectors intersect at a single point, the <strong>circumcentre</strong> of <code class='latex inline'>\triangle QRS</code>.</p><p><strong>c)</strong> Find the distance from each vertex of <code class='latex inline'>\triangle QRS</code> to the circumcentre.</p><p><strong>d)</strong> Describe the circle that passes through the vertices of <code class='latex inline'>\triangle QRS</code></p><p><strong>e)</strong> Describe how you would use geometry software to answer parts a) to d).</p>
<p>Find the coordinates of the midpoint, <code class='latex inline'>M</code>, of <code class='latex inline'>AB</code>.</p><img src="/qimages/746" />
<p><strong>(a)</strong> Verify that the points <code class='latex inline'>A(12, 6), B(4, 10)</code>, and <code class='latex inline'>C(0, 2)</code> lie on a circle with its centre at <code class='latex inline'>D(6, 4)</code>.</p><p><strong>(b)</strong> Determine the length of the radius of the circle.</p>
<p>What is the radius of the circle below?</p><p><code class='latex inline'>9x^2+9y^2=16</code></p>
<p>For each equation of a circle:</p><p><strong>i)</strong> Determine the radius.</p><p><strong>ii)</strong> State the x- and y-intercepts.</p><p><code class='latex inline'>x^2+y^2=0.04</code></p>
<p>Describe the region defined by each inequality. Then. draw and label a diagram of the three regions.</p><p> <code class='latex inline'>x^2 + y^2 < 25</code></p>
<p>Write the equation of a circle with centre <code class='latex inline'>(0,0)</code> and radius <code class='latex inline'>r</code>.</p><p><code class='latex inline'>r=400</code></p>
<p>The graph shows a circle with its centre at (0,0).</p><img src="/qimages/715" /><p><strong>a)</strong> State the x-intercepts of the circle.</p><p><strong>b)</strong> State the y-intercepts.</p><p><strong>c)</strong> State the radius.</p><p><strong>d)</strong> Write the equation of the circle.</p>
<p>Is the following points are on the circle with equation <code class='latex inline'>x^2+y^2=65</code>? Explain.</p><p><code class='latex inline'>(8,-1)</code></p>
<p>Write the equation of a circle with centre <code class='latex inline'>(0,0)</code> and radius <code class='latex inline'>r</code>.</p><p><code class='latex inline'>r=50</code></p>
<p><strong>(a)</strong> Verify that the points <code class='latex inline'>E(-5, 0), F(-2, 3)</code>, and <code class='latex inline'>G(6, -11)</code> lie on a circle with its centre at <code class='latex inline'>H(2, -4)</code>.</p><p><strong>(b)</strong> Determine the length of the radius of the circle.</p>
<p>A ship drops its anchor into the water and creates a circular ripple. The radius of this ripple increases at a rate of <code class='latex inline'>50 cm/s</code>.</p> <ul> <li> A small rowboat is <code class='latex inline'>50</code>m east and 75 m north of the point where the anchor was dropped. How long does the ripple take to reach the rowboat?</li> </ul>
<p>Verify that the line through the origin and the midpoint of the chord <code class='latex inline'>R(-3, 6)</code> and <code class='latex inline'>S(-6, -3)</code> is perpendicular to the chord of <code class='latex inline'>x^2 + y^2 = 45</code></p>
<ul> <li>State the coordinates of the centre of the circle described by each equation below.</li> <li>State the radius and the x— and y—intercepts of the circle.</li> <li>Sketch a graph of the circle.</li> </ul> <p><code class='latex inline'> \displaystyle x^2 + y^2 = 98 </code></p>
<p>A circle has its centre at <code class='latex inline'>(0,0)</code> and passes through the point <code class='latex inline'>(8,15)</code>.</p><p><strong>a)</strong> Calculate the radius of the circle.</p><p><strong>b)</strong> Write an equation for the circle.</p><p><strong>c)</strong> Sketch the graph.</p>
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