Question:
If the eccentricity of the standard hyperbola passing through the point $(4,6)$ is 2 , then the equation of the tangent to the hyperbola at $(4,6)$ is-
Correct Option: 1
Solution:
Let us Suppose equation of hyperbola is
$\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$
$\mathrm{e}=2 \Rightarrow \mathrm{b}^{2}=3 \mathrm{a}^{2}$
passing through $(4,6) \Rightarrow \mathrm{a}^{2}=4, \mathrm{~b}^{2}=12$
$\Rightarrow$ equaiton of tangent
$x-\frac{y}{2}=1$
$\Rightarrow 2 x-y-2=0$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.