Question

The coordinates of the middle point of the chord cut-off by $2x-5y+18=0$ by the circle $x^2+y^2-6x+2y-54=0$ are

• A. $(1,4)$
• B. $(2,4)$
• C. $(4,1)$
• D. $(1,1)$

Answer 1

Answer: (A)

$(1,4)$

Center of the circle is $(3,-1)$

Co-ordinates of middle point will be foot of the perpendicular from center to $2x-5y+18=0$

$\frac{x-3}{2}=\frac{y+1}{-5}=-\left(\frac{2\left(3\right)-5(-1)+18}{2^2+5^2}\right)=-1$

Therefore, $(x,y)=(1,4)$.