Question

Which of the following is a point on the common chord of the circles $x^{2} + y^{2} + 2x - 3y + 6 = 0$ and $x^{2} + y^{2} + x - 8y - 13 = 0$

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

Answer 1

Answer: (D)

(1, – 4)

Answer 2

Given circles are, $S_{1} \equiv x^{2} + y^{2} + 2x - 3y + 6 = 0$ ….. (i)

and $S_{2} \equiv x^{2} + y^{2} + x - 8y - 13 = 0$ ….. (ii)

$\therefore$ Equation of common chord is $S_{1} - S_{2} = 0$

$\Rightarrow x + 5y + 19 = 0$, and out of the four given points only point (1, – 4) satisfies it