Find the gradient of line between (2ap, ap^2) and (2aq, aq^2)

If P is the point (a,b) and ! is the point (-b, a) and O is the origin, show that OP is perpendicular to OQ

Question

Find the gradient of line between (2ap, ap^2) and (2aq, aq^2) 

If P is the point (a,b) and ! is the point (-b, a) and O is the origin, show that OP is perpendicular to OQ

mww · Answer

gradient use 
$$m = \frac{ y_2 - y_1 }{ x_2 - x_1 }$$
and simplify by factorising and cancelling

OP is perpendicular to OQ if their gradients multiply to give -1:
$$mOP \times mOQ = -1$$

So find the gradient of OP and OQ and multiply them.