Question

Find the equation of the straight lines whose value of p =2√2 ,alpha=225degrees

Answer 1

Step-by-step explanation:

Given,

$p = 2 \sqrt{2} \: \: and \: \: \alpha = \frac{5\pi}{4}$

Here, 225 degree=(180+45) degree=(π+(π/4))=(5π)/4

So,we have,

$x \cos( \alpha ) + y \sin( \alpha ) = p$

$= > x \cos( \frac{5\pi}{4} ) + y \sin( \frac{5\pi}{4} ) = 2 \sqrt{2}$

$= > x \cos(\pi + \frac{\pi}{4} ) + y\sin(\pi + \frac{\pi}{4} ) = 2 \sqrt{2}$

$= > - x \cos( \frac{\pi}{4} ) - y \sin( \frac{\pi}{4} ) = 2\sqrt{2}$

$= > - \frac{x}{ \sqrt{2} } - \frac{y}{ \sqrt{2} } = 2\sqrt{2}$

Multiplying both side by √2, we get,

$= > - x - y = 4$

$= > x + y + 4 = 0$

Hope this will help you..!