If a curve passes through the point (1, --2) and has slope of the tangent at any point (x,…

Question

If a curve passes through the point (1, --2) and has slope of the tangent at any point (x, y) on it as $${{{x^2} - 2y} \over x}$$, then the curve also passes through the point :

Accepted Answer

$${{dy} \over {dx}} = {{{x^2} - 2y} \over x}$$                    (Given)

$${{dy} \over {dx}} + 2{y \over x} = x$$

I.F = $${e^{\int {{2 \over x}dx} }} = {x^2}$$

$$ \therefore $$  y.x2 = $$\int {x.{x^2}} dx + C$$

= $${{{x^4}} \over y} + C$$

This curve passes through (1, - 2) $$ \Rightarrow $$  C= - $${9 \over 4}$$

$$ \therefore $$  yx2 = $${{{x^4}} \over 4} - {9 \over 4}$$

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

Solutions · 1