Question

Write the equation in the center-radius form for a circle with center (−1,0) and radius 6

A) (x+1)²+y²=36
B) (x−1)²+y²=6
C) (x+1)²+y²=6
D) (x−1)²+y² =36

Answer 1

The equation of the circle with center (-1,0) and radius 6 is (x + 1)² + y² = 36, which corresponds to Option A.

Step-by-step explanation:

The question asks to write the equation of a circle in center-radius form given the circle's center and radius. The general form for a circle's equation is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius of the circle.

For a circle with a center at (−1, 0) and a radius of 6, the equation becomes:

(x - (−1))² + (y - 0)² = 6²

Simplifying this, we have:

(x + 1)² + y² = 36

Therefore, the correct equation is Option A: (x + 1)² + y² = 36.