Question

Identify the center and radius of y²+11=-2y-x2+8x

Answer 1

Compare the equation of circle with general equation if a circle, x^2+y^2+2gx+2fy+c=0. This is obtained using the concept of locus of the point that satisfies the definition of circle(Point that moves such that its distance from a point is fixed.) (x-a) ^2+(y-b)^2=r.

Comparing(both are eq of same locus) we have, a=-g, b=-f r= underroot(g^2+f^2-c)

Here, a=-(-4) =4 b=-1, r=( 16+1-11)^1/2=root 6