Question

lf the polars of the points $(x_1,y_1)$ and $(x_2,y_2)$ w.r. to the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ are at right angles then $\frac{x_1{x}_2}{y_1{y}_2}=$

• A. $\frac{-a^3}{b^3}$
• B. $\frac{4a^4}{b^4}$
• C. $\frac{a^4}{4b^4}$
• D. $\frac{-a^4}{b^4}$

Answer 1

The correct option is D $\frac{-a^4}{b^4}$

$\frac{x_{1}x}{a^2}-\frac{y_{1}y}{b^2}=1$
$y^1/l_1=\frac{x_1{b}^2}{a^2{y}_1}=m_1$
$\frac{x_{2}x}{a^2}-\frac{y_{2}y}{b^2}=1$
$y^1/l_2=\frac{x_2{b}^2}{a^2{y}_2}=m_2$
$m_1{m}_2=1$
$\frac{x_1{x}_2}{y_2{y}_1}=-\frac{a^4}{b^4}$