Math  /  Geometry

QuestionWrite the standard form of the equation of the circle with the given center and radius. Center (5,7),r=8(-5,7), r=8
Type the standard form of the equation of the circle. (Simplify your answer.)

Studdy Solution

STEP 1

1. The center of the circle is given as (5,7)(-5, 7).
2. The radius of the circle is 88.

STEP 2

1. Recall the standard form of the equation of a circle.
2. Substitute the given center and radius into the equation.
3. Simplify the equation.

STEP 3

Recall the standard form of the equation of a circle:
(xh)2+(yk)2=r2 (x - h)^2 + (y - k)^2 = r^2
where (h,k)(h, k) is the center of the circle and rr is the radius.

STEP 4

Substitute the given center (5,7)(-5, 7) and radius 88 into the equation:
(x(5))2+(y7)2=82 (x - (-5))^2 + (y - 7)^2 = 8^2

STEP 5

Simplify the equation:
(x+5)2+(y7)2=64 (x + 5)^2 + (y - 7)^2 = 64
The standard form of the equation of the circle is:
(x+5)2+(y7)2=64 \boxed{(x + 5)^2 + (y - 7)^2 = 64}

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