Q198 / 270 · NDA 2023 (Phase 2) · Mathematics

Given that $4 x^2+y^2=9$ What is the maximum value of xy?

  • Correct answer
    A
    $\frac{9}{4}$
  • B
    $\frac{3}{2}$
  • C
    $\frac{4}{9}$
  • D
    $\frac{2}{3}$

Solution

Since, $y= \pm \sqrt{9-4 x^2}$ let $f(x)=x y=x \sqrt{9-4 x^2}$ So, maximum value of $f(x)$ is $\frac{9}{4}$

Hence, the correct answer is option: 'A'.

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