Question

If $y=x$ and $3y+2x=0$ are the equations of a pair of conjugate diameters of an ellipse, then the eccentricity of the ellipse is

• A. $\sqrt{\frac{2}{3}}$
• B. $\frac{1}{\sqrt{3}}$
• C. $\frac{1}{\sqrt{2}}$
• D. $\frac{2}{\sqrt{5}}$

Answer 1

The correct option is B $\frac{1}{\sqrt{3}}$

$m_1{m}_2=\frac{-b^2}{a^2}(m_1{m}_2$ are the slopes of conjugate diameters )

$m_1=1,m_2=\frac{-2}{3}$

$\frac{b^2}{a^2}=\frac{2}{3}$

$e^2=1-\frac{2}{3}$

$e=\frac{1}{\sqrt{3}}$