JEE PYQ: Application Of Derivatives Question 78
Question 78 - 2019 (12 Jan Shift 1)
If a curve passes through the point $(1, -2)$ and has slope of the tangent at any point $(x, y)$ on it as $\frac{x^2 - 2y}{x}$, then the curve also passes through the point:
(1) $(3, 0)$
(2) $(\sqrt{3}, 0)$
(3) $(-1, 2)$
(4) $(-\sqrt{2}, 1)$
Show Answer
Answer: (2)
Solution
$\frac{dy}{dx} + \frac{2y}{x} = x$. I.F. $= x^2$. Solution: $x^2 y = \frac{x^4}{4} + C$. Through $(1,-2)$: $C = -\frac{9}{4}$. Curve: $y = \frac{x^2}{4} - \frac{9}{4x^2}$. At $(\sqrt{3}, 0)$: $\frac{3}{4} - \frac{9}{12} = 0$. Verified.
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