x2 /a2+ y2/b2 = 1 show that d2y/ dx2 = - b4/a2y3 - Maths - Continuity and Differentiability

Question

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

Priyanka Kedia · Accepted Answer

x2a2+y2b2=1Differentiating w r
t x, we have,1a2ddxx2+1b2ddxy2=ddx1⇒1a22x+1b22ydydx=0⇒xa2+yb2dydx=0        
2⇒dydx=-xb2a2yAgain differentiating w r
t x, we have,ddxxa2+ddxyb2dydx=0⇒1a2+1b2yd2ydx2+dydx2=0⇒yd2ydx2+dydx2=-b2a2⇒d2ydx2=-b2a2-dydx2y⇒d2ydx2=-b2a2--xb2a2y2y⇒d2ydx2=-b2a2-x2b4a4y2y⇒d2ydx2=-b2a2y2-x2b4a4y2×y⇒d2ydx2=-a2y2b2+x2b4a4y3⇒d2ydx2=-b4a4y3