Question

The diameter of the circle $x^{2} + y^{2} - 4x + 2y - 11 = 0$ corresponding to a system of chords parallel to the line $x - 2y + 1 = 0$

• A. $x - 2y + 3 = 0$
• B. $2x - y + 3 = 0$
• C. $2x + y - 3 = 0$
• D. None of these

Answer 1

Answer: (C)

$2x + y - 3 = 0$

Answer 2

The centre of the given circle is (2, –1) the equation of the line perpendicular to chord $x - 2y + 1 = 0$ is $2x + y + k = 0$

Since the line passes through the point (2, –1)

therefore k = – 3. The equation of diameter is $2x + y - 3 = 0.$