Product of lengths of perpendiculars drawn from any point on hyperbola {x^2} - 2{y^2} - 2 = 0 to its

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10-2. Parabola, Ellipse, Hyperbola

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The product of the lengths of perpendiculars drawn from any point on the hyperbola ${x^2} - 2{y^2} - 2 = 0$ to its asymptotes is

A

$1\over2$

B

$2\over3$

C

$3\over2$

D

$2$

Solution

(b) Given equation is $\frac{{{x^2}}}{2} – \frac{{{y^2}}}{1} = 1$…..$(i)$

Product of length of perpendiculars drawn from any point on the hyperbola $(i)$ to the asymptotes is

$\frac{{{a^2}{b^2}}}{{{a^2} + {b^2}}}= \frac{{2 \times 1}}{{2 + 1}} = \frac{2}{3}$.

Standard 11

Mathematics

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