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Standard XII

Mathematics

Condition of Concurrency of 3 Straight Lines

PM and PN are...

Question

PM and PN are the perpendiculars from any point P on the rectangular hyperbola $x y = c^{2}$ to the asymptotes.

If the locus of the mid point of MN is a conic, then its eccentricity is

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Solution

The correct option is B

OMPN is rectangle.

$P = (c t, \frac{c}{t})$

Mid point $= (\frac{c t}{2}, \frac{c}{2 t}) = (x, y) ∴ x y = \frac{c^{2}}{4} \Rightarrow e = \sqrt{2}$

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PM and PN are the perpendiculars from any point P on the rectangular hyperbola xy=c2 to the asymptotes. If the locus of the mid point of MN is a conic, then its eccentricity is

The correct option is B OMPN is rectangle. P=(ct,ct) Mid point =(ct2,c2t)=(x,y) ∴ xy=c24⇒e=√2

PM and PN are the perpendiculars from any point P on the rectangular hyperbola $x y = c^{2}$ to the asymptotes.

If the locus of the mid point of MN is a conic, then its eccentricity is

The correct option is B

OMPN is rectangle.

$P = (c t, \frac{c}{t})$

Mid point $= (\frac{c t}{2}, \frac{c}{2 t}) = (x, y) ∴ x y = \frac{c^{2}}{4} \Rightarrow e = \sqrt{2}$