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

Answer 1

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.