The correct option is D (18, −116)
Differentiating y2=2x3, we get
2ydydx=6x2⇒dydx=3x2y
The slope of the line 4x - 3y +2 = 0 is 43. Therefore, the coordinates of P(x, y) must satisfy
3x2y.43 = -1⇒4x2=−y
Also, y2=2x3 . Solving these, we get x = 18and y = -116 (clearly x ≠0)