If $a{x^2} + 2hxy + b{y^2} = 1$, then $\frac{{{d^2}y}}{{d{x^2}}}$ equals

$\frac{{{h^2} - ab}}{{{{\left( {hx + by} \right)}^2}}}$

JEE MATHEMATICS MCQ: DIFFERENTIATION

1 Hard

1 of 1

Analyzing +4 | -1

a{x^2} + 2hxy + b{y^2} = 1

, then

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

equals

View answer and explanation

Correct option: D

\frac{{{h^2} - ab}}{{{{\left( {hx + by} \right)}^3}}}

Option D is correct because the second derivative is found by implicit differentiation and simplification, resulting in

\frac{{{h^2} - ab}}{{{{\left( {hx + by} \right)}^3}}}

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