13.
Find the parabola with vertex (-2, 5) and focus (2, 6)
<span>(x-h)^2=4p(y-k), (h,k)=(x,y)
</span><span>coordinates of the vertex axis of symmetry: x=-2
</span><span>p=1 (distance above vertex on the axis of symmetry)
4p=4
</span>(x + 2)^2 = 4 (y - 5)
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14. W<span>hat is the center and radius of a circle with the given equation?
</span><span>x2</span>+4x+<span>y2</span>−10y−7=<span>0
</span>Move all variables to the left side and all constants to the right side.<span><span>x2</span>+4x+<span>y2</span>−10y=7+<span>0
</span></span>Add <span>77</span> and <span>00</span> to get <span>77</span>.<span><span>x2</span>+4x+<span>y2</span>−10y=<span>7
</span></span>Complete the square<span> for </span><span><span><span>x2</span>+4x</span><span><span>x2</span>+4x</span></span><span>.
</span><span><span>(x+2)</span>2</span>−<span>4
</span>
Substitute <span><span><span><span>(x+2)</span>2</span>−4</span><span><span><span>(x+2)</span>2</span>-4</span></span> for <span><span><span>x2</span>+4x</span><span><span>x2</span>+4x</span></span> in the equation <span><span><span>x2</span>+4x+<span>y2</span>−10y=7</span><span><span>x2</span>+4x+<span>y2</span>-10y=7</span></span>.<span><span><span>
(x+2)</span>2</span>−4+<span>y2</span>−10y=<span>7
</span></span>Move <span><span>−4</span><span>-4</span></span> to the right side of the equation by adding <span>44</span> to both sides.<span><span><span>(x+2)</span>2</span>+<span>y2</span>−10y=7+<span>4
</span></span>Complete the square<span> for </span><span><span><span>y2</span>−10y</span><span><span>y2</span>-10y</span></span><span>.
</span><span><span>(y−5)</span>2</span>−<span>25
</span>Substitute <span><span><span><span>(y−5)</span>2</span>−25</span><span><span><span>(y-5)</span>2</span>-25</span></span> for <span><span><span>y2</span>−10y</span><span><span>y2</span>-10y</span></span> in the equation <span><span><span>x2</span>+4x+<span>y2</span>−10y=7</span><span><span>x2</span>+4x+<span>y2</span>-10y=7</span></span>.<span><span><span>
(x+2)</span>2</span>+<span><span>(y−5)</span>2</span>−25=7+<span>4
</span></span>Move <span><span>−25</span><span>-25</span></span> to the right side of the equation by adding <span>2525</span> to both sides.<span><span><span>(x+2)</span>2</span><span><span>(y−5)</span>2</span>=7+4+<span>25
</span></span>Add <span>77</span> and <span>44</span> to get <span>1111</span>.<span><span><span>(x+2)</span>2</span>+<span><span>(y−5)</span>2</span>=11+<span>25
</span></span>Add <span>1111</span> and <span>2525</span> to get <span>3636</span>.<span><span><span>(x+2)</span>2</span>+<span><span>(y−5)</span>2</span>=<span>36
</span></span>This is the form of a circle. Use this form to determine the center and radius of the circle.<span><span><span>(x−h)</span>2</span>+<span><span>(y−k)</span>2</span>=<span>r<span>2
</span></span></span>Match the values in this circle to those of the standard form. The variable <span>rr</span> represents the radius of the circle, <span>hh</span> represents the x-offset from the origin, and <span>kk</span> represents the y-offset from origin.<span><span>r=6</span><span>r=6</span></span><span><span>h=−2</span><span>h=-2</span></span><span>k=<span>5
</span></span>These values represent the important values for graphing and analyzing a circle.Center: <span>(−2,5)(-2,5)</span>Radius: 6
Find the parabola with vertex (-2, 5) and focus (2, 6)
<span>(x-h)^2=4p(y-k), (h,k)=(x,y)
</span><span>coordinates of the vertex axis of symmetry: x=-2
</span><span>p=1 (distance above vertex on the axis of symmetry)
4p=4
</span>(x + 2)^2 = 4 (y - 5)
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14. W<span>hat is the center and radius of a circle with the given equation?
</span><span>x2</span>+4x+<span>y2</span>−10y−7=<span>0
</span>Move all variables to the left side and all constants to the right side.<span><span>x2</span>+4x+<span>y2</span>−10y=7+<span>0
</span></span>Add <span>77</span> and <span>00</span> to get <span>77</span>.<span><span>x2</span>+4x+<span>y2</span>−10y=<span>7
</span></span>Complete the square<span> for </span><span><span><span>x2</span>+4x</span><span><span>x2</span>+4x</span></span><span>.
</span><span><span>(x+2)</span>2</span>−<span>4
</span>
Substitute <span><span><span><span>(x+2)</span>2</span>−4</span><span><span><span>(x+2)</span>2</span>-4</span></span> for <span><span><span>x2</span>+4x</span><span><span>x2</span>+4x</span></span> in the equation <span><span><span>x2</span>+4x+<span>y2</span>−10y=7</span><span><span>x2</span>+4x+<span>y2</span>-10y=7</span></span>.<span><span><span>
(x+2)</span>2</span>−4+<span>y2</span>−10y=<span>7
</span></span>Move <span><span>−4</span><span>-4</span></span> to the right side of the equation by adding <span>44</span> to both sides.<span><span><span>(x+2)</span>2</span>+<span>y2</span>−10y=7+<span>4
</span></span>Complete the square<span> for </span><span><span><span>y2</span>−10y</span><span><span>y2</span>-10y</span></span><span>.
</span><span><span>(y−5)</span>2</span>−<span>25
</span>Substitute <span><span><span><span>(y−5)</span>2</span>−25</span><span><span><span>(y-5)</span>2</span>-25</span></span> for <span><span><span>y2</span>−10y</span><span><span>y2</span>-10y</span></span> in the equation <span><span><span>x2</span>+4x+<span>y2</span>−10y=7</span><span><span>x2</span>+4x+<span>y2</span>-10y=7</span></span>.<span><span><span>
(x+2)</span>2</span>+<span><span>(y−5)</span>2</span>−25=7+<span>4
</span></span>Move <span><span>−25</span><span>-25</span></span> to the right side of the equation by adding <span>2525</span> to both sides.<span><span><span>(x+2)</span>2</span><span><span>(y−5)</span>2</span>=7+4+<span>25
</span></span>Add <span>77</span> and <span>44</span> to get <span>1111</span>.<span><span><span>(x+2)</span>2</span>+<span><span>(y−5)</span>2</span>=11+<span>25
</span></span>Add <span>1111</span> and <span>2525</span> to get <span>3636</span>.<span><span><span>(x+2)</span>2</span>+<span><span>(y−5)</span>2</span>=<span>36
</span></span>This is the form of a circle. Use this form to determine the center and radius of the circle.<span><span><span>(x−h)</span>2</span>+<span><span>(y−k)</span>2</span>=<span>r<span>2
</span></span></span>Match the values in this circle to those of the standard form. The variable <span>rr</span> represents the radius of the circle, <span>hh</span> represents the x-offset from the origin, and <span>kk</span> represents the y-offset from origin.<span><span>r=6</span><span>r=6</span></span><span><span>h=−2</span><span>h=-2</span></span><span>k=<span>5
</span></span>These values represent the important values for graphing and analyzing a circle.Center: <span>(−2,5)(-2,5)</span>Radius: 6