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Two equal parabolas have the same vertex and their axes are at right angles. Prove that their common tangent touches each at the end of their latus rectum.
Solution please.
Dear Ravi,
Ans: The 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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