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 \(\frac{23}{3}\)