Question

Equation of a tangent to the hyperbola $5 x^{2}-y^{2}=5$ and which passes through an external point $(2,8)$ is
(A) $3 x-y+2=0$
(B) $3 x+y-14=0$
(C) $23 x-3 y-22=0$
(D) $3 x-23 y+178=0$

Answer 1

Ans: $(\mathrm{A}, \mathrm{C})$
Hint : Let the tangent be $\quad \mathrm{y}=\mathrm{mx} \pm \sqrt{\mathrm{m}^{2}-5}$
Since it passes through $(2,8) \quad \Rightarrow(8-2 m)^{2}=m^{2}-5$
$\Rightarrow 3 m^{2}-32 m+69=0 \quad \Rightarrow 3 m^{2}-9 m-23 m+69=0 \Rightarrow(3 m-23)(m-3)=0 \quad \Rightarrow m=3$ or $\frac{23}{3}$