Find the set of values of K for which the equation ` zbarz + ( -3 +4i) barz-(3-4i) z+K =0` represents a circle.

Options

A. `(-infty, 25]`
B. `[25,infty)`
C. `[5,infty)`
D. `(-infty,5)`

Answer

A

Explanation

We have,
`zbarz+(-3+4i)barz+(-3-4i)z+k=0`
The represents a circle with center at `(3-4i)` and Radius `=sqrt(|-3+4i|^(2)-k)=sqrt(25-k)`
For the circle to exist, we msut have
`25-k ge 0 rArr k le 25`
Hence, the given equation will represent a circle, if `k le 25`.