Q105 / 155 · WBJEE 2024 · Mathematics

The locus of the midpoint of the system of parallel chords parallel to the line $y=2 x$ to the hyperbola $9 x^2-4 y^2=36$ is

A
8x - 9y = 0
Correct answer
B
9x - 8y = 0
C
8x + 9y = 0
D
9x - 4y = 0

Solution

Hint : Locus implies diameter of the hyperbola $\begin{aligned} & \text {i.e. } y=\frac{b^2}{a^2 m} x \quad(m=2) \\ & \Rightarrow y=\frac{9}{8} x \\ & \Rightarrow 9 x-8 y=0 \end{aligned}$

Hence, the correct answer is option: 'B'.

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