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Grade: 11
        

Prove that an infinite number of triangles can be inscribed in either of the parabolas y^2=4ax and x^2=4by whose sides touch the other

10 years ago

Answers : (1)

Ramesh V
70 Points
							

For the 2 parabolas: y2=4ax and x2=4by intersect at 2 points

A(0,0) and B[ 4*(ab2)1/3,(4*(a2b)1/3) ]  which lie on common chord y = (a/b)1/3*x

for any general point ( at2,2at) on y2=4ax where t is parameter

and for any general point ( am2,2am) on x2=4ay where m is parameter

there can be infinite points taken on both these parabolas and can form triangles with the common chord

y = (a/b)1/3*x

 

 

10 years ago
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