Write the equation of the circle centered at ( − 8 , − 4 ) that passes through ( 15 ,− 8 )?

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Write the equation of the circle centered at ( − 8 , − 4 ) that passes through ( 15 ,− 8 )?

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Answer 1 · 2018-05-14T19:09:16

${(x + 8)}^{2} + {(y + 4)}^{2} = 545$ $(x+8)^2+(y+4)^2=545$

Explanation:

Your circle has the equation of ${(x - x_{c})}_{c}^{2} + {(y - y_{c})}_{c}^{2} = r^{2}$ $(x-x_c)^2 + (y-y_c)^2 = r^2$
where $x_{c}$ $x_c$ is the value of x of the center, and $y_{c}$ $y_c$ is the value of y of the center and r is the radius. So here where the center is at (-8, -4), you circle is ${(x + 8)}^{2} + {(y + 4)}^{2} = r^{2}$ $(x+8)^2+(y+4)^2=r^2$
Time to find the radius (r):
Your circle passes through (15,-8) which means that ${(15 + 8)}^{2} + {(- 8 + 4)}^{2} = r^{2}$ $(15+8)^2+(-8+4)^2=r^2$
$\Rightarrow 23^{2} + {(- 4)}^{2} = r^{2}$ $=> 23^2+(-4)^2=r^2$
$\Rightarrow r^{2} = 525$ $=> r^2=525$
So finally, your circle is: ${(x + 8)}^{2} + {(y + 4)}^{2} = 545$ $(x+8)^2+(y+4)^2=545$

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Write the equation of the circle centered at ( − 8 , − 4 ) that passes through ( 15 ,− 8 )?

1 Answer

Explanation:

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