Find the area of the triangle formed in the right half-plane by the lines $x-y=0$ and $x+y=0$, and a tangent to the hyperbola $x^2-y^2=a^2$, where $a$ is a non-zero number.
🎥 Video solution / Text Solution of this question is given below:
The lines
$x-y=0$ and $x+y=0$
are the asymptotes of the hyperbola
$x^2-y^2=a^2$.
For a hyperbola, the area of the triangle formed by any tangent and its two asymptotes is constant.