Question

4x^2+12x+4y^2-8y=87
what is the center and radius?

Answer 1

C = (-3/2, 1)

r = 25

Explanation:

4x² + 12x + 4y² - 8y = 87 divide both sides by 4

x² + 3x + y² - 2y = 87/4 rearrange the equation

(x² + 3x + h) + (y² - 2y + k) = 87/4 + h + k complete the square

h = (3/2)² = 9/4

k = (-2/2)² = 1

(x² + 3x + 9/4) + (y² -2y + 1) = 87/4 + 9/4 + 1

(x² + 3x + 9/4) + (y² -2y + 1) = 25

(x + 3/2)² + (y - 1)² = 25

r² = 25

r = √25 = 5

C = (h, k) = (-3/2, 1)