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Let \mathrm{y=m x+2 \sqrt{5}} is a tangent to the hyperbola \mathrm{4 x^2-y^2=16. } Find the equation of a diameter of the hyperbola bisecting the chords parallel of the tangent.

Option: 1

4 x \pm 5 y=0


Option: 2

3 x \pm 5 y=0


Option: 3

4 x \pm 3 y=0


Option: 4

\text { None of these }


Answers (1)

best_answer

The equation of hyperbola is \mathrm{\frac{x^2}{4}-\frac{y^2}{16}=1}

\mathrm{y=m x+2 \sqrt{5}} touches the hyperbola \mathrm{(2 \sqrt{5})^2=4 m^2-16}

\mathrm{\Rightarrow m^2=9 \Rightarrow m= \pm 3}

So, the required equation of a diameter is

\mathrm{ y=\frac{16 x}{4( \pm 3)} \Rightarrow 4 x \pm 3 y=0 }

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Rishi

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