For the real parameter

MATHEMATICS · Subjective · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

k

, consider the equation

x^{2}+y^{2}+2(3-k)x+2(4+k)y+(k^{2}-25)=0.

(i) Rewrite the equation in completed–square form. (ii) Derive the condition on

k

for which the equation represents a circle with a real (non–imaginary) radius. (iii) For such values of

k

, find the corresponding centre and radius of the circle. (iv) What geometric figure is represented when

k

is chosen so that the radius becomes zero?