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Question

Question: If line lx + my + n = 0 cuts the ellipse \(\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}}\)= 1 at points ...

If line lx + my + n = 0 cuts the ellipse x2a2+y2b2\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}}= 1 at points whose eccentric angle differ by π2\frac{\pi}{2}, then value of product of slopes of lines joining origin to these points is

A

Depends on l only

B

Depends on m only

C

Depends on n only

D

Independent of l, m, n

Answer

Independent of l, m, n

Explanation

Solution

Lines joining origin to such points are conjugate diameters & product of their slopes is b2a2\frac{- b^{2}}{a^{2}} which satisfy (4) option