Question

Find the coordinate of the circle of the centre and its radius if its equation is

(a) x² + y² - 12y + 6 = 0

(b) -2x² - 2y² - 18y + 9 = 0

Answer 1

Answer:-

general equation : x²+y²+2gx+2fy+c=0

(a) x² + y² - 12y + 6 = 0

Centre= (-g,-f)= (0,6)

Radius=$\sqrt{g^2+f^2-c}$ =$\sqrt{0+36-6}$

=5.4

(b) -2x² - 2y² - 18y + 9 = 0

deciding by -2

We get x²+y²+9y+4.5=0

Centre= (-g,-f)= (0,-4.5)

Radius=$\sqrt{g^2+f^2-c}$

=$\sqrt{0+(4.5)^2-4.5}$

=3.96