Find equation of circle with center on a line y= - x has radius 4 and passes through origin?

1 Answer
Mar 5, 2018

Equation of circle is x^2+y^2+4sqrt2x-4sqrt2y=0

Explanation:

As circle passes thrugh origin, its cinstant term ought to be 0 and hence equation is of the type

x^2+y^2+2gx+2fy=0, whose center is (-g,-f) and radius is sqrt(g^2+f^2)

As center (-g,-f) lies on y=-x,

we have -f=-(-g) or f=-g

and aas radius is 4, we have sqrt(g^2+f^2)=4

or 2g^2=16 i.e. g=sqrt8=2sqrt2 and f=-2sqrt2

and equation of circle is x^2+y^2+4sqrt2x-4sqrt2y=0

graph{(x^2+y^2+4sqrt2x-4sqrt2y)(y+x)=0 [-12.79, 7.21, -2.92, 7.08]}