QJEEM19Ma613a: JEE Main 2019 Mathematics - Class 12 JEEM19Ma613a Solution: If a curve passes through the point (1, –2) and has slope of…

Question

Verified Solution • 2025–26 Session moderate

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} - 2 y}{x}

, then the curve also passes through the point :

Accepted Answer

\frac{d y}{d x} = \frac{x^{2} - 2 y}{x}

(Given)

\frac{d y}{d x} + 2 \frac{y}{x} = x

I.F =

e^{\int \frac{2}{x} d x} = x^{2}

∴

y.x² =

\int x . x^{2} d x + C

=

\frac{x^{4}}{y} + C

This curve passes through (1,

-

2)

\Rightarrow

C=

-

\frac{9}{4}

∴

yx² =

\frac{x^{4}}{4} - \frac{9}{4}

Now check option(s), Which is satisly by option (ii)

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