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Analytical Geometry

Cool goIITian

Joined:	10 Jul 2007
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25 Nov 2007 23:35:57 IST

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sahya----

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Let P(p) and Q(q) be two distinct points. Let R and S be the points dividing PQ internally and exterenly in the ratio 2:3 . If OR is perpendicular to OS, then show that 9p^2=4q^2.

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sowjanya gudipati

Cool goIITian

Joined: 13 Oct 2007

Posts: 75

26 Nov 2007 21:34:44 IST

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let the point p be (x₁,y₁) this gives p²=x₁²+y₁² andthe point q be (x₂, y₂) this gives q²=x₂²+y₂²

ponit R=(3x₁+2x₂/5 , 2y₂+3y₁/5) point Q=(3x₁-2x₂ , 3y₁-2y₂)

OR*OS=-1

this gives 9y₁²-4y₂²/9x₁²-4x₂²=-1

this gives 9x₁²+9y₁²=4x₂²+4x₁²

therefore 9P²=4Q²

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