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A circle in the
xy-plane has its center at
(-4,5) and the point
(-8,8) lies on the circle. Which equation represents this circle?

A circle in the $x y$ -plane has its center at $(-4,5)$ and the point $(-8,8)$ lies on the circle. Which equation represents this circle?

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Write equations of circles in standard form using properties

Full solution

Q. A circle in the

x y

-plane has its center at

(-4,5)

and the point

(-8,8)

lies on the circle. Which equation represents this circle?

Identify Center and Point: Identify the center (h, k) and a point on the circle to find the radius. $\newline$ Center: ( $-4$ , $5$ ) $\newline$ Point on circle: ( $-8$ , $8$ ) $\newline$ Calculate the radius using the distance formula: $r = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ $\newline$ $r = \sqrt{((-8) - (-4))^2 + (8 - 5)^2}$ $\newline$ $r = \sqrt{(-4)^2 + 3^2}$ $\newline$ $r = \sqrt{16 + 9}$ $\newline$ $r = \sqrt{25}$ $\newline$ $r = 5$
Calculate Radius: Substitute the values of h, k, and r into the standard form equation of a circle. $\newline$ Standard form: $(x - h)^2 + (y - k)^2 = r^2$ $\newline$ Substitute h = $-4$ , k = $5$ , and r = $5$ . $\newline$ $(x - (-4))^2 + (y - 5)^2 = 5^2$ $\newline$ $(x + 4)^2 + (y - 5)^2 = 25$

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