y2=px3+q...(i) Differentiating both sides w.r.t. x, we get y⋅
dy
dx
=3px2 ⇒
dy
dx
=
3p
2
(
x2
y
) ∴(
dy
dx
)(2,3)=
3p
2
×
4
3
=2p Slope of the line y=4x−5 is 4 . Since the line touches the curve, their slopes are equal. ∴2p=4⇒p=2 Since (2,3) lies on y2=px3+q. ∴2p=4⇒p=2 Since (2,3) lies on y2=px3+q. ∴9=2×8+q⇒q=−7 ∴p−q=2+7=9