In ellipse frac{{{x^2}}}{{{a^2}}} + frac{{{y^2}}}{{{b^2}}} = 1 , equation of diameter conjugate to d

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10-2. Parabola, Ellipse, Hyperbola

easy

In the ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$, the equation of diameter conjugate to the diameter $y = \frac{b}{a}x$, is

A

$y = - \frac{b}{a}x$

B

$y = - \frac{a}{b}x$

C

$x = - \frac{b}{a}y$

D

None of these

Solution

(a) $y = \frac{{ – b}}{a}x$

(Two diameter $y = {m_1}x$ and $y = {m_2}x$ will be conjugate diameter,if ${m_1}{m_2} = – \frac{{{b^2}}}{{{a^2}}}$).

Standard 11

Mathematics

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