Question

The coordinates of the middle points of the chord cut-off by $2x-y+18=0$ by the circle $x^2+y^2-6x+2y-54=0$ are

• A. $(-7,4)$
• B. $(2,4)$
• C. $(4,1)$
• D. none of these

Answer 1

The correct option is A $(-7,4)$

Let the $(h,k)$ be the mid point
Then equation of chord is given by $S_1=S_{1}1$
$\Rightarrow hx+ky-3(h+x)+y+k-54=0$
$\Rightarrow (h-3)x+(k+1)y-3h+k-54=0$
comparing with $2x-y+18=0$
$\frac{h-3}{2}=\frac{k+1}{-1}=\frac{-3h+k-54}{18}$
On solving we get $(h,k)=(-7,4)$