Q108 / 160 · TS EAMCET 2022 (20 Jul Shift 2) · Mathematics

If $y=\frac{a x+b}{c x+d}$, than $\frac{d x}{d y}=$

  • A
    $\frac{a d-b c}{(a x+b)^2}$
  • Correct answer
    B
    $\frac{a d-b c}{(a-c y)^2}$
  • C
    $\frac{a d+b c}{(c x+d)^2}$
  • D
    $\frac{a d+b c}{(a+c y)^2}$

Solution

Given $y=\frac{a x+b}{c x+d}$ $\Rightarrow \mathrm{x}=\frac{\mathrm{b}-\mathrm{yd}}{\mathrm{yc}-\mathrm{a}}$ $\text { now } \frac{\mathrm{dx}}{\mathrm{dy}}=\frac{\mathrm{ad}-\mathrm{bc}}{(\mathrm{yc}-\mathrm{a})^2}$

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

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