Question

What's the equation of tangent on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ at the point $(4\sqrt{2},3)?$

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

For a hyperbola the equation of tangent at a point

$p(x_1,y_1)$ is obtained by formula,

$T_1=0$

Where $T_1)$ is an experssion obtained by replacing

$x^{2}byx{x}_1$

$y^{2}byy{y}_1$

$xby\frac{x+x_1}{2}$

$yby\frac{y+y_1}{2}$

in the given equation of the hyperbola.

For a hyperbola in standard form $T_1$ is given by

$\frac{x{x}_1}{a^2}-\frac{y{y}_1}{b^2}$

For the given hyperbola,

$\frac{x^2}{16}-\frac{y^2}{9}=1$

The tangent is given by,

$\frac{x{x}_1}{16}-\frac{y{y}_1}{9}=1$

$\frac{4\sqrt{2}.x}{{16}_4}-\frac{3.y}{9.3}=1$

$3\sqrt{2}x-4y-12=0$

Hence option (d) is correct

This method of taking $T_1=0$ as tangent is ture

for all types of conics including the circle.