Grade 11IIT JEE Entrance Exam
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?
1 Answer
Deepak Kumar Shringi
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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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.
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