Question

Find the product of the length of perpendiculars drawn from any point on the hyperbola `x^2-2y^2-2=0` to its asymptotes.
A. `1//2`
B. `2//3`
C. `3//2`
D. `2`

Answer 1

We have,
`(x^(2))/((sqrt(2))^(2))-(y^(2))/(1)=1`........`(i)`
We know that the product of the lengths of perpendicular from any point on the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1` to its asymptotes is
`(a^(2)b^(2))/(a^(2)+b^(2))`
Here, `a^(2)=2` and `b^(2)=1`. So, required product `=(2)/(2+1)=(2)/(3)`