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Prove that two parabolas having same focus but opposite faced cut at right angles?

Prove that two parabolas having same focus but opposite faced cut at right angles? 

Grade:11

1 Answers

Deepak Kumar Shringi
askIITians Faculty 4404 Points
5 years ago
he parabolas are y²=4ax & x²=4ay.

The tangent of the first parabola at a point (a,-2a) i.e at the one end of the latus rectum is y= x+a putting this value at the other equation we get, it cuts the other parabola at the point (-2a,a) i.e at the extremity of the latus rectum. Hence prooved. ( You should note that I have used the direct formulae of the tangent equation YY1=2a(X+X1) )



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