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:

Question

Aicharya · Accepted Answer

Let us suppose equation of hyperbola is
$\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$
$e = 2$

$∵ b^{2} = (e^{2} - 1) a^{2}$

$\Rightarrow b^{2} = 3 a^{2}$
It is passing through $(4,6)$

$\frac{16}{a^{2}} - \frac{36}{b^{2}} = 1$

$\Rightarrow a^{2} = 4, b^{2} = 12$
So, equation of tangent is $T = 0$

$\frac{x x_{1}}{a^{2}} - \frac{y y_{1}}{b^{2}} = 1$

Tangent at point $(4, 6)$ is
$\Rightarrow x - \frac{y}{2} = 1$
$\Rightarrow 2 x - y - 2 = 0$

If the eccentricity of the standard hyperbola passing through the point ( 4,6 ) is 2 , then the equation of…

Solution