If the line ky − 2x − k2 + 2h = 0 & parabola x2 = 4y touches each other, then
k4(−k2 + 2h) = 4
Solving these two equations
ky − 2x − k2 + 2h = 0 - - - - - - - - - (1) & parabola x2 = 4y −−−−−−−(2) is
substituting y = x24 in equation (1)
k.x24 − 2x − k2 + 2h = 0
k4x2 − 2x − k2 + 2h
since ,it touches to parabola ;there should be only one root
discriminant (D)=0
b2 − 4ac = 0
4 − 4 × (k4).(−k2 + 2h) = 0
1 − (k4)(−k2 + 2h) = 0
k4(−k2 + 2h) = 4