Correct Answer - Option 2 : y
2 = 2x
Concept:
Let the mid point of chord of the parabola y2 = 4ax is (h, k)
The equation of chord passing through the mid point of the chord of the parabola is given by T = S1 i.e yk - 2a(x + h) = k2 - 4ah, where T is the tangent and S1 is equation of the parabola which we get by replacing y and x by k and h respectively.
Calculation:
compare the parabola y2 = 4x with parabola y2 = 4ax, we get a = 1
chord passes through vertex (0, 0) so this point satisfy chord equation
⇒ 0 - 2(0 + h) = k2 - 4h
⇒ k2 = 2h
Now replace h by x and k by y in the above equation, we get
y2 = 2x