If α=π2,then the equation xcosα+ysinα=pbecomes

α=π2,xcosα+ysinα=pxcosπ2+ysinπ2=p⇒x(0)+y(1)=p⇒y=p∴ Equation of a line parallel to x-axis.

If α=π2,then the equation xcosα+ysinα=pbecomes

α=π2,xcosα+ysinα=pxcosπ2+ysinπ2=p⇒x(0)+y(1)=p⇒y=p∴ Equation of a line parallel to x-axis.

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If $α = \frac{π}{2},$ then the equation $x \cos α + y \sin α = p$ becomes

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Equation of X-axis

Equation of a line parallel to X-axis

Equation of Y-axis

Equation of a line parallel to Y-axis

answer is B.

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$α = \frac{π}{2}, x \cos α + y \sin α = p$

$x \cos \frac{π}{2} + y \sin \frac{π}{2} = p$

$\Rightarrow x (0) + y (1) = p$

$\Rightarrow y = p$

$∴$ Equation of a line parallel to x-axis.

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If α=π2,then the equation xcosα+ysinα=pbecomes

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If $α = \frac{π}{2},$ then the equation $x \cos α + y \sin α = p$ becomes