1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16Question 6IncorrectYour answer is incorrect.Try againFind an equation of the circle that has center −6, 1 and passes through −2, 5.

The equation of a circle is given by the formula (x-h)² + (y-k)² = r², where (h, k) is the center of the circle and r is the radius.

Given that the center of the circle is (-6, 1), we can substitute h = -6 and k = 1 into the equation to get:

(x - (-6))² + (y - 1)² = r² which simplifies to: (x + 6)² + (y - 1)² = r²

We also know that the circle passes through the point (-2, 5). We can substitute x = -2 and y = 5 into the equation to solve for r²:

(-2 + 6)² + (5 - 1)² = r² which simplifies to: 4² + 4² = r² 16 + 16 = r² 32 = r²

So, the equation of the circle that has center (-6, 1) and passes through (-2, 5) is:

(x + 6)² + (y - 1)² = 32