Question

If $x=9$ is a chord of contact of the hyperbola $x^2-y^2=9$, the the equation of the tangent at one of the points of contact is

• A. $x+\sqrt{3}y+2=0$
• B. $3x-2\sqrt{2}y-3=0$
• C. $3x-\sqrt{2}y+6=0$
• D. $x-\sqrt{3}y+2=0$

Answer 1

The correct option is B $3x-2\sqrt{2}y-3=0$

$x=9$ is chord of cortact

Of $x^2-y^2=9$ ...(1)

Put $x=9$ in rquation (1)

$\Rightarrow 81-y^2=9$

$\Rightarrow y^2=72\Rightarrow y=\pm 6\sqrt{2}$

So, one of the point of contact is $(9,6\sqrt{2})$

tangent at $9,6\sqrt{2}$ is

$\frac{x,x_1}{a^2}-\frac{y{y}_1}{b^2}=1$

$x\times 9-y\times 6\sqrt{2}=9$

$3x-2\sqrt{2}y=3$