Question

If the curves $x^2+p{y}^2=1andq{x}^2+y^2=1$ are orthogonal to each other then

• A. $p-q=2$
• B. $\frac{1}{p}-\frac{1}{q}=2$
• C. $\frac{1}{p}+\frac{1}{q}=-2$
• D. $\frac{1}{p}+\frac{1}{q}=2$

Answer 1

The correct option is D

$\frac{1}{p}+\frac{1}{q}=2$

Solving the two equations

$\frac{x^2}{y^2}=\frac{p-1}{q-1}-------\left(1\right)$
$m_1.m_2=-1\Rightarrow \frac{x^2}{y^2}.\frac{q}{p}=-1$
$\Rightarrow \frac{1}{p}+\frac{1}{q}=2$