Parabola Tangent 2

Question

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.

Askiitians Expert Soumyajit IIT-Kharagpur · Accepted Answer

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) ) Please feel free to post as many doubts on our discussion forum as you can. If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE preparation. All the best Ravi !!! Regards, Askiitians Experts SOUMYAJIT IIT_KHARAGPUR

Analytical Geometry> Parabola Tangent 2...

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.

Ravi Malhotra , 14 Years ago

Askiitians Expert Soumyajit IIT-Kharagpur

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Analytical Geometry> Parabola Tangent 2...

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.

Ravi Malhotra , 14 Years ago

Askiitians Expert Soumyajit IIT-Kharagpur

LIVE ONLINE CLASSES

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