Question

The equation of a tangent to the hyperbola $4x^2-5y^2=20$ parallel to the line $x-y=2$ is :

• A. $x-y+1=0$
• B. $x-y+7=0$
• C. $x-y-3=0$
• D. $x-y+9=0$

Answer 1

The correct option is A $x-y+1=0$

The tangent to the hyperbola $\frac{x^2}{5}-\frac{y^2}{4}=1$ is
$y=mx\pm \sqrt{5m^2-4}$
The tangent is parallel to the line $x-y=2$ therefore, they have same slope.
$\Rightarrow m=1$
Hence, $y=x\pm \sqrt{5-4}$
$y=x\pm 1$
$\Rightarrow y=x+1$ or $y=x-1$
$x-y+1=0$ and $x-y-1=0$