Consider the equation

MATHEMATICS · Multi-part · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

x^2 + y^2 + 2kx - 4y + (k^2 - 5) = 0

, where

k

is a real parameter. (i) Find the range of

k

for which this equation represents a real circle. (ii) For

k = 3

, calculate the radius of the circle.