Q72 / 150 · MHT CET 2021 (21 Sep Shift 1) · Mathematics

The equation of a line passing through $(\rho \cos \propto, p \sin \propto)$ and making an angle $(90+\propto)$ with positive direction of $\mathrm{X}$-axis is

  • A
    $x \cos \propto-y \sin \propto=2 p$
  • B
    $x \sin \propto+y \cos \propto=p$
  • Correct answer
    C
    $x \cos \propto+y \sin \propto=p$
  • D
    $\mathrm{x} \cos \propto+\mathrm{y} \sin \propto=3 \mathrm{p}$

Solution

Slope of line $=\tan (90+\propto)=-\cot \propto$ Equation of required line is $$ \begin{aligned} & (y-p \sin \propto)=\frac{-\cos \propto}{\sin \propto}(x-p \cos \propto) \\ & \therefore(\sin \propto) y-p \sin ^2 \propto=(-\cos \propto) x+p \cos ^2 \propto \\ & \therefore(\operatorname{Cos} \propto) x+(\sin \propto) y=p \end{aligned} $$

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

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