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show that y^2 = ax^2 + bx +c then y^3(d^2y/dx^2) is constant

show that  y^2 = ax^2 + bx +c then y^3(d^2y/dx^2) is constant

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
6 years ago
Ans:
y = \sqrt{ax^{2}+bx+c}
\frac{dy}{dx} = \frac{2ax+b}{2\sqrt{ax^{2}+bx+c}}
\frac{d^{2}y}{dx^{2}} = \frac{4ac-b^{2}}{4(ax^{2}+bx+c)^{3/2}}
y^{3}.\frac{d^{2}y}{dx^{2}} = (ax^{2}+bx+c)^{3/2}.\frac{4ac-b^{2}}{4(ax^{2}+bx+c)^{3/2}} = \frac{4ac-b^{2}}{4}
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty

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