How do you write and equation for a circle with Center: (-4, 9) and radius: 12?

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How do you write and equation for a circle with Center: (-4, 9) and radius: 12?

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Answer 1 · 2016-06-25T07:20:34

$x^{2} + y^{2} + 8 x - 18 y - 47 = 0$ $x^2+y^2+8x-18y-47=0$

Explanation:

The equation of a circle with center at $(h, k)$ $(h,k)$ and radius $r$ $r$ is

${(x - h)}^{2} + {(y - k)}^{2} = r^{2}$ $(x-h)^2+(y-k)^2=r^2$ (this is equivalent to distance of a point on circumference from center being equal to radius).

Hence the equation of a circle with center at $(- 4, 9)$ $(-4,9)$ and radius $12$ $12$ is

${(x - (- 4))}^{2} + {(y - 9)}^{2} = 12^{2}$ $(x-(-4))^2+(y-9)^2=12^2$ or

$(x + 4))^{2} + {(y - 9)}^{2} = 144$ $(x+4))^2+(y-9)^2=144$ or

$x^{2} + 8 x + 16 + y^{2} - 18 y + 81 = 144$ $x^2+8x+16+y^2-18y+81=144$ or

$x^{2} + y^{2} + 8 x - 18 y + 97 - 144 = 0$ $x^2+y^2+8x-18y+97-144=0$ or

$x^{2} + y^{2} + 8 x - 18 y - 47 = 0$ $x^2+y^2+8x-18y-47=0$

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How do you write and equation for a circle with Center: (-4, 9) and radius: 12?

1 Answer

Explanation:

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