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Ravi Malhotra Grade: 10
        

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.

6 years ago

Answers : (1)

Askiitians Expert Soumyajit IIT-Kharagpur
28 Points
										

 


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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Regards,


Askiitians Experts


SOUMYAJIT IIT_KHARAGPUR

6 years ago
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