Q107 / 200 · TS EAMCET 2001 · Mathematics

The family of curves in which the sub-tangent at any point to any curve is double the abscissa is given by

  • Correct answer
    A
    $x=C y^2$
  • B
    $y=C x^2$
  • C
    $x^2=C y^2$
  • D
    $y^2=C x^3$

Solution

The length of sub-tangent $=y \cdot \frac{d x}{d y}$ Given, $\quad y \frac{d x}{d y}=2 x$ $\Rightarrow \quad \frac{d x}{x}=2 \frac{d y}{y}$ $\Rightarrow \quad \log x=2 \log y+\log C$ $\Rightarrow \quad x=C y^2$

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

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