Question

Which of the following is the equation of the circle with centre (-1.5, 0.5) and radius 3?

A. 2x^2 + 6x + 2y^2 - 2y - 13 = 0

B. 2x^2 - 6x + 2y^2 + 2y - 13 = 0

C. 2x^2 - 6x + 2y^2 - 2y - 13 = 0

D. 2x^2 + 6x + 2y^2 - 2y - 23 = 0

E. @x^2 + 6x + 2y^2 - 2y -14 = 0

Answer 1

C(-1.5,0.5), P(x,y)

r^2 = (x+1.5)^2 + (y-0.5)^2 = 3^2
x^2+3x+2.25 + y^2-y+0.25 = 9
x^2+3x + y^2-y = 9-2.25-0.25 = 6.5
x^2+3x=(3/2)^2 + y^2-y+(-1/2)^2 = 6.5
x^2+3x+9/4 + y^2-y+1/4 = 26/4+9/4+1/4
x^2+3x+9/4 + Y^2-y+1/4 = 36/4
Multiply both sides by 4:
4x^2+12x+9 + 4y^2-4y+1 = 36
4x^2+12x + 4y^2-4y-26 = 0
Divide both sides by 2:
2x^2+6x + 2y^2-2y-13 = 0