Verified Answer :

caylus

Hello,
Let (a,b) the intersection of the tangent and the curve.
That point must be double.

So
 b=ma
b²=a-c
==>(ma)²-a+c=0
==>m²a²-a+c=0 roots must be equal
Δ=(-1)²-4m²c=0 => 4m²c=1==>c=1/(4m²)

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