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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
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
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
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