Question

The equation of the tangent to the curve $4 x^2-9 y^2=1$ which is parallel to $4 y=5 x+7$ is

(a) $24 y-30 x=17$

(b) $30 y-24 x= \pm \sqrt{161}$

(c) $24 y-30 x= \pm \sqrt{161}$

(d) None of these

Answer 1

Here $m=\frac{5}{4}$ and $a^2=\frac{1}{4}, b^2=\frac{1}{9}$

$\therefore$ Equation of tangent is $y=m x \pm \sqrt{a^2 m^2-b^2}$

$\therefore \quad y=\frac{5}{4} x \pm \sqrt{\frac{1}{4} \times \frac{25}{16}-\frac{1}{9}}=\frac{5}{4} x \pm \frac{\sqrt{161}}{24}$

$\Rightarrow \quad 24 y-30 x= \pm \sqrt{161}$

So, The correct option of this question will be (C).