If x = at2 and y = 2at, find y2 at t = 2.

We have,      x = at2dxdt = 2 at     y = 2atdydt = 2anow,      dydx = dydt×dtdx = 2a2at = 1td2ydx2 = -1t2×dtdx = -1t2×12at = -12at3d2ydx2t=2 = -12a23 = - 116a

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y2 = 2a, hence its a constant for values of t.

THerefore, y2 = 2a , at t=2,

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