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  • If the product of the perpendicular distances from any point on the hyperbola <img alt="\mathrm{\frac{x^2}{a^2}-\frac{y^2}{b^2}=1}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B

If the product of the perpendicular distances from any point on the hyperbola \mathrm{\frac{x^2}{a^2}-\frac{y^2}{b^2}=1} of eccentricity \mathrm{e=\sqrt{3}} from its asymptotes is equal to 6 , then the length of the transverse axis of the hyperbola is

Option: 1

3


Option: 2

6


Option: 3

8


Option: 4

12


Answers (1)

best_answer

\mathrm{\mathrm{p}_1 \mathrm{p}_2=\frac{\mathrm{a}^2 \mathrm{~b}^2}{\mathrm{a}^2+\mathrm{b}^2}=\frac{\mathrm{a}^2 \cdot \mathrm{a}^2\left(\mathrm{e}^2-1\right)}{\mathrm{a}^2 \mathrm{e}^2}=6}

\mathrm{\frac{2 a^2}{3}=6 \Rightarrow a^2=9 \Rightarrow a=3}

\mathrm{\text { hence } 2 a=6}

Posted by

Ritika Kankaria

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