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Question: The asymptotes of the hyperbola \(\frac{x^{2}}{a^{2}}\) – \(\frac{y^{2}}{b^{2}}\) = 1 make an angle ...

The asymptotes of the hyperbola x2a2\frac{x^{2}}{a^{2}} – y2b2\frac{y^{2}}{b^{2}} = 1 make an angle of 300 with x-axis then equation of diameter conjugate to the diameter y = 2x-

A

x – 2y = 0

B

3x – 2y = 0

C

x – 6y = 0

D

None of these

Answer

x – 6y = 0

Explanation

Solution

Slope of xa−yb\frac{x}{a} - \frac{y}{b} = 1 is ba\frac{b}{a} = tan 30° Ž ba\frac{b}{a} = 13\frac{1}{\sqrt{3}}

Slope of one diameter is m1 = 2

Two diameter are conjugate if m1m2 = b2a2\frac{b^{2}}{a^{2}}

\ 2m2 = 1/3

Ž m2 = 1/6

Ž other diameter is y = x6\frac{x}{6}, x – 6y = 0.