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Question

If y2=ax2+bx+c, then y3.d2ydx2 is

A
A constant
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B
A function of x only
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C
A function of y only
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D
A function of x and y
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Solution

The correct option is D A constant
y2=ax2+bx+c .......... (1)

Differentiate w.r.t x

2yy1=2ax+b .......... (2)
Here, y1=dydx

Again, diff w.r.t to x

2y21+2yy2=2a

y21+yy2=a ............. (3)

y2y21+y3y2=a(ax2+bx+c) using (2)

(ax+b2)2+y3y2=a2x2+abx+ac

a2x2+abx+b24+y3y2=a2x2+abx+ac

y3y2=acb24

y3y2=4acb24 is a constant.

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