Question

the perpendicular distance from the origin is 5cm and slope is -1.find the equation of the line and also the angle

Answer 1

Let c be the intercept on the y-axis.
Then, the equation of the line is

y=−x+c       [∵m=−1]⇒x+y=c⇒x12+12√+y12+12√=c12+12√            [Dividing both sides by (coefficient of x)2+(coefficient of y)2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√]⇒x2√+y2√=c2√    

This is the normal form of the given line.
Therefore, c2√ denotes the length of the perpendicular from the origin.
But, the length of the perpendicular is 5 units.

∴ ∣∣c2√∣∣=5⇒c=±52‾√

Thus, substituting c=±52‾√ in y=−x+c, we get the equation of line to be y=−x+52‾√  or, x+y−52‾√=0