If the straight line y=m x+c touches the parabola y^2-4 a x+4 a^3=0 , then c is

Step-by-step solution

Solving the given equations, aligned &(m x+c)^2=4 a x-4 a^3 & m^2 x^2+2 m c x+c^2=4 a x-4 a^3 & m^2 x^2+(2 m c-4 a) x+c^2+4 a^3=0 aligned Since the straight line touches the parabola at a point, so, the discriminant =0 aligned & (2 m c-4 a)^2-4 m^2 (c^2+4 a^3 )=0 & 4 m^2 c^2-16 a m c+16 a^2-4 m^2 c^2-16 a^3 m^2=0 & -m c+a-a^2 m^2=0 & m c=a-a^2 m^2 c= a m -a^2 m aligned