Mathematics

Problem

A curve is defined parametrically by the equations

x=t^2

and

y=t^3

. A variable pair of perpendicular lines through the origin

O

meet the curve at

P

and

Q

. If the locus of the point of intersection of the tangents at

P

and

Q

ay^2=bx-1

, then the value of

(a+b)

is.....