Question

Which of the following is the standard equation of a circle with center (-1,-6) and radius 5?

Answer 1

(x + 1)^2 + (y + 6)^2 = 25.

Explanation:

• The standard equation of a circle with center (h, k) and radius r is given by:

(x - h)^2 + (y - k)^2 = r^2

• In this case, the center of the circle is (-1, -6) and the radius is 5. Substituting these values into the equation, we get:

(x - (-1))^2 + (y - (-6))^2 = 5^2

• Simplifying and rearranging terms, we get:

(x + 1)^2 + (y + 6)^2 = 25

• Therefore, the standard equation of the circle with center (-1, -6) and radius 5 is (x + 1)^2 + (y + 6)^2 = 25.