Write the standard form of the equation of the specified circle. Center: (-6, 1); solution point: (-2, 4)?

Question

Write the standard form of the equation of the specified circle. Center: (-6, 1); solution point: (-2, 4)?

Answer 1

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

This is the standard equation of a circle. To find h and k, you need to know the origin. Luckily, they already gave you the origin: (-6, 1). You know: (h, k) is the origin, so:

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

Now, to find r^2, we need to use the distance formula. Use the origin and the solution point to find it.

r = [(x2-x1)^2 + (y2-y1)^2]^1/2

r = [(-2 + 6)^2 + (4-1)^2]^1/2

r = [(4)^2 + (3)^2]^1/2

r = [16 + 9]^1/2

r = [25]^1/2

r = 5

r^2 = 25

Now that you have r^2, just plug it in:

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

Hope that helps!