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

1 Answer
Theodossis Papadopoulos
May 14, 2018

(x+8)^2+(y+4)^2=545(x+8)2+(y+4)2=545

Explanation:

Your circle has the equation of (x-x_c)^2 + (y-y_c)^2 = r^2(x−xc)2+(y−yc)2=r2
where x_cxc is the value of x of the center, and y_cyc 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=r2
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=r2
=> 23^2+(-4)^2=r^2⇒232+(−4)2=r2
=> r^2=525⇒r2=525
So finally, your circle is: (x+8)^2+(y+4)^2=545(x+8)2+(y+4)2=545

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