Question

Equation of one of the tangents passing through $(2,8)$ to the hyperbola $5x^2-y^2=5$ is

• A. $3x+y-14=0$
• B. $3x-y+2=0$
• C. $x+y+3=0$
• D. $x-y+6=0$

Answer 1

Answer: (B)

$3x-y+2=0$

Hyperbola is $\frac{x^2}{1}-\frac{y^2}{5}=1$,

Equation of tangent is $y=mx\pm \sqrt{m^2-5}$

$(2,8)$ lies on this line

So,$(8-2m{)}^2=(m^2-5)$

$\Rightarrow m=3$

So, $y=3x\pm \sqrt{9-5}$

$\Rightarrow y=3x\pm \sqrt{4}$

$\Rightarrow 3x-y=\pm 2$

$\Rightarrow 3x-y+2=0$ is the tangent