Question:
The equation of a tangent to the hyperbola $4 x^{2}-5 y^{2}=20$ parallel to the line $x-y=2$ is:
Correct Option: 1
Solution:
(1) Given, the equation of line,
$x-y=2 \Rightarrow y=x-2$
$\therefore$ its slope $=m=1$
Equation of hyperbola is:
$\frac{x^{2}}{5}-\frac{y^{2}}{4}=1$
$\Rightarrow a^{2}=5, b^{2}=4$
The equation of tangent to the hyperbola is,
$y=m x \pm \sqrt{a^{2} m^{2}-b^{2}}$\
$=x \pm \sqrt{5-4}$
$\Rightarrow y=x \pm 1$