Question

The area of the circle $x^2 - 2x + y^2 - 10\,y + k = 0$ is $25 \pi $ . The value of k is equal to

• A. -1
• B. 1
• C. 0
• D. 2
• E. 3

Answer 1

Answer: (B)

We have,
$x^{2}-2 x+y^{2}-10\, y+k=0$
$\therefore $ Radius $=\sqrt{g^{2}+f^{2}-c}$
$=\sqrt{(1)^{2}+(5)^{2}-k}$
$=\sqrt{1+25-k}$
$=\sqrt{26-k}$
$\therefore $ Area of circle $=\pi$ (Radius) $^{2}$
$\therefore 25 \pi=\pi(\sqrt{26-k})^{2}$
$ \Rightarrow 25 \pi =\pi(26-k) $
$ \Rightarrow 25 =26-k $
$\Rightarrow k =1$