Math  /  Geometry

Questionx2+(y+6)2=36x^{2}+(y+6)^{2}=36

Studdy Solution

STEP 1

1. The equation represents a geometric shape.
2. The equation is in the standard form of a circle.

STEP 2

1. Identify the geometric shape.
2. Determine the center of the circle.
3. Determine the radius of the circle.

STEP 3

Identify the geometric shape represented by the equation:
The equation x2+(y+6)2=36 x^{2} + (y+6)^{2} = 36 is in the form of (xh)2+(yk)2=r2 (x-h)^{2} + (y-k)^{2} = r^{2} , which is the standard form of a circle.

STEP 4

Determine the center of the circle:
The center (h,k)(h, k) of the circle is derived from the equation (xh)2+(yk)2=r2 (x-h)^{2} + (y-k)^{2} = r^{2} . Here, h=0 h = 0 and k=6 k = -6 .
Thus, the center of the circle is (0,6) (0, -6) .

STEP 5

Determine the radius of the circle:
The radius r r is the square root of the right-hand side of the equation. Here, r2=36 r^{2} = 36 , so r=36=6 r = \sqrt{36} = 6 .
The circle has a center at (0,6) (0, -6) and a radius of 6 6 .

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