Q109 / 160 · TS EAMCET 2015 · Mathematics
The product of lengths of perpendicular from any point on the hyperbola $x^2-y^2=16$ to its asymptotes, is
- A2
- B4
- Correct answerC8
- D16
Solution
We know that, the product of lengths of perpendicular from any point on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ to its asymptotes is $\frac{a^2 b^2}{a^2+b^2}$.
Given, equation of hyperbola is
$$
\begin{aligned}
x^2-y^2 & =16 \\
\quad \frac{x^2}{(4)^2}-\frac{y^2}{(4)^2} & =1
\end{aligned}
$$
Here, $a=4$ and $b=4$
Now, $\quad \frac{a^2 b^2}{a^2+b^2}=\frac{16 \times 16}{16+16}=\frac{16 \times 16}{2 \times 16}=8$
Hence, the correct answer is option: 'C'.