Q230 / 270 · NDA 2022 (Phase 1) · Mathematics

What does the equation $x \frac{d y}{d x}-2 y=0$ represent?

  • A
    A family of straight lines
  • B
    A family of circles
  • Correct answer
    C
    A family of parabolas
  • D
    A family of ellipses

Solution

$\begin{aligned} & x \frac{d y}{d x}-2 y=0 \\ & x \frac{d y}{d x}=2 y\end{aligned}$ $\int \frac{1}{\mathrm{y}} \mathrm{dy}=2 \int \frac{1}{\mathrm{x}} \mathrm{dx}$ $\begin{aligned} & \ell \text { ny }=2 \ln x+\ell \mathrm{nc} \\ & \ell \text { ny }=\ell \mathrm{nx}^2+\ell \mathrm{nc} \\ & \ell \mathrm{n} y=\ell \mathrm{n}\left(\mathrm{cx}^2\right) \\ & \mathrm{y}=\mathrm{cx}^2\end{aligned}$ It represent the equation of parabolas.

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

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