Find the equation of a line for which p = 8, α = 225°

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Givenp = 8, α = 225°Concept Used:Equation of line in normal form.

Explanation:So, the equation of the line in normal form is

Formula Used:x cos α + y sin α = p x cos 225° + y sin 225° = 8

We know, cos (180° + θ) = – cos θ , sin (180° + θ) = – sin θ

⇒ – cos 45° – y sin 45° = 8

⇒ \(-\frac{x}{\sqrt{2}}-\frac{y}{\sqrt{2}}=8\)

⇒ x + y + 8√2 = 0

Hence, the equation of line in normal form is x + y + 8√2 = 0