Question

If the circle $x^2+y^2-17x+2fy+c=0$ passes through $(3,1),(14,-1)$ and $(11,5)$, then $c$ is

• A. $0$
• B. $-41$
• C. $-17/2$
• D. $41$

Answer 1

Answer: (D)

Given equation of circle is
$x^2+y^2-17x+2fy+c=0$.
Since it passes through $(3,1)$, $(14,-1)$ and $(11,5)$
$\therefore 9+1-51+2f+c=0$
or $2f+c=41$ $...(i)$
and $196+1-238-2f+c=0$
or $-2f+c=41$ $...(ii)$
Adding $(i)$ and $(ii)$, we get
$2c=\left(2\times 41\right)$
or $c=41$.