x2 /a2+ y2/b2 = 1 show that d2y/ dx2 = - b4/a2y3

x2a2+y2b2=1Differentiating w.r.t x, we have,1a2ddxx2+1b2ddxy2=ddx11a22x+1b22ydydx=0xa2+yb2dydx=0        .....2dydx=-xb2a2yAgain differentiating w.r.t x, we have,ddxxa2+ddxyb2dydx=01a2+1b2yd2ydx2+dydx2=0yd2ydx2+dydx2=-b2a2d2ydx2=-b2a2-dydx2yd2ydx2=-b2a2--xb2a2y2yd2ydx2=-b2a2-x2b4a4y2yd2ydx2=-b2a2y2-x2b4a4y2×yd2ydx2=-a2y2b2+x2b4a4y3d2ydx2=-b4a4y3

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