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Q.

If y2=ax2+bx+c, then y3d2ydx2 is

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a

a constant

b

a function of x only

c

a function of y only

d

a function of x and y

answer is A.

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Detailed Solution

2ydydx=2ax+b2dydx2+2yd2ydx2=2ayd2ydx2=a−dydx2=a−2ax+b2y2=4ay2−(2ax+b)24y2⇒4y3d2ydx2=4aax2+bx+c−4a2x2+4abx+b2⇒4y3d2ydx2=4ac−b2=constant

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