Question

The equation of a tangent to the hyperbola $x^2-2y^2=18$, which is perpendicular to the line $x-y=0$, is :

• A. $x+y=3$
• B. $x+y+2=0$
• C. $x+y=3\sqrt{2}$
• D. $x+y+3\sqrt{2}=0$

Answer 1

Answer: (A)

$x+y=3$

Equation of line perpendicular to $x-y=0$ is given by
$y=-x+c$
Also this line is tangent to the hyperbola $x^2-2y^2=18$
So we have $m=-1,a^2=18,b^2=9$
Thus Using condition of tangency $c^2=a^2{m}^2-b^2=18-9=9\Rightarrow c=\pm 3$
Hence required equation of tangent is $x+y=\pm 3$