Question

The product of the lengths of perpendiculars drawn from any point on the hyperbola x² – 2y² – 2 = 0 to its asymptotes, is-

• A. ½
• B. 2/3
• C. 3/2
• D. 2

Answer 1

Answer: (B)

2/3

Answer 2

Given equation is x² – 2y² – 2 = 0, it can be rewritten as $\frac{x^{2}}{2} - \frac{y^{2}}{1} = 1$

Here a² = 2, b² = 1

We know that equation of hyperbola is $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}}$ = 1, then the product of length of perpendicular drawn from any point on the hyperbola to the asymptotes is $\frac{a^{2}b^{2}}{a^{2} + b^{2}} = \frac{2(1)}{2 + 1} = \frac{2}{3}$.