Question

A circle $x ^ { 2 } + y ^ { 2 } + 2 g x + 2 f y + c = 0$ passing through $( 4 , - 2 )$ is concentric to the circle $x ^ { 2 } + y ^ { 2 } - 2 x + 4 y + 20 = 0$, then the value of c will be.

• A. – 4
• B. 4
• C. 0
• D. 1

Answer 1

Answer: (A)

– 4

Answer 2

Circle $x ^ { 2 } + y ^ { 2 } + 2 g x + 2 f y + c = 0$ is concentric with $x ^ { 2 } + y ^ { 2 } - 2 x + 4 y + 20 = 0$. Therefore centre is $( 1 , - 2 )$ and radius $= \sqrt { g ^ { 2 } + f ^ { 2 } - c } = \sqrt { ( 1 - 4 ) ^ { 2 } + ( - 2 + 2 ) ^ { 2 } }$ $\Rightarrow c = - 4$.