Question

For the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,$ the equation of the diameter conjugate to $ax-by=0$ is

• A. $bx+ay=0$
• B. $bx-ay=0$
• C. $a^{3}y+b^{3}x=0$
• D. $a^{3}y-b^{3}x=0$

Answer 1

Answer: (C)

$a^{3}y+b^{3}x=0$

$m_1=\frac{a}{b}$ and $m_1{m}_2=-\frac{b^2}{a^2}$
$\Rightarrow m_2=-\frac{b^3}{a^3}$
$\Rightarrow \frac{y}{x}=-\frac{b^3}{a^3}$
$\Rightarrow a^{3}y+b^{3}x=0$
Ans: C