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

1.	Find the equation of a line for which p = 8, α = 225°
Answer» Given p = 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

Answer»

Given p = 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

Discussion