Question

The equation of polar of the hyperbola
$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ with respect to the pole $(x_1,y_1)$ is

• A. $\frac{x{x}_1}{a^2}-\frac{y{y}_1}{b^2}=1$
• B. $\frac{x{x}_1}{a^2}-\frac{y{y}_1}{b^2}=2$
• C. $\frac{x{x}_1}{a^2}-\frac{y{y}_1}{b^2}=\frac{1}{a^2+b^2}$
• D. $\frac{x{x}_1}{a^2}+\frac{y{y}_1}{b^2}=\frac{1}{a^2+b^2}$

Answer 1

The correct option is A $\frac{x{x}_1}{a^2}-\frac{y{y}_1}{b^2}=1$

Consider a variable point P inside or outside hyperbola and tangents drawn to the hyperbola from P touch hyperbola at points Q and R. Then the locus of point of intersection of tangents at Q and R is called polar.
Point P is called the pole.
$\frac{x{x}_1}{a^2}-\frac{y{y}_1}{b^2}=1$ is the equation of polar, where $(x_1,y_1)$ is the pole.