Question

In the equation of ellipse given in $(\ast )$ if $a^2=\frac{5}{3},b^2=\frac{5}{4}$ then the equation of the diameter conjugate to the diameter $y+3x=0$ is

• A. $x-4y=0$
• B. $x-5y=0$
• C. $x-3y=0$
• D. None of these

Answer 1

Answer: (A)

$x-4y=0$

Equation of ellipse, for the given values of $a^2$ and $b^2$ is written as $\frac{x^2}{5/3}+\frac{y^2}{5/4}=1$ and that of diameter is given by $y=-3x$
So the equation of conjugate diameter is
$y=m_{2}x$ where $m_1{m}_2=\frac{-b^2}{a^2}$
$\Rightarrow -3m_2=\frac{-3}{4}\therefore m_2=\frac{1}{4}$
$\therefore$ Equation of conjugate diameter is $4y-x=0$.