Q. Which of the following is a point on the common chord of the circle $x^{2} + y^{2} + 2x - 3y + 6 = 0$and$x^{2} + y^{2} + x - 8y - 13 = 0$?
A) $(1,\ - 2)$
B) (1, 4)
C) (1, 2)
D) $(1,\ - 4)$
Explanation
(d)
$\therefore$ equation of common chord is
$\left( x^{2} + y^{2} + 2x - 3y + 6 \right) - \left( x^{2} + y^{2} + x - 8y - 13 \right) = 0$
$\lbrack\because S_{1} - S_{2} = 0\rbrack$
$\Rightarrow \ \ \ x + 5y + 19 = 0$
In the given option, only the point $(1,\ - 4)$ satisfies this equation
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.