Question

the locus of the point of intersection of perpendicular straight lines which are at constant distance 'P' from the origin is ​

Answer 1

Answer:

$x^{2} + y^{2} = P^{2}$

Step-by-step explanation:

Let the Point of Intersection$(POI)$ be $(x,y)$

It is given that the lines maintain a constant distance "$P$" from the origin

⇒ Distance of the $POI$ from the $Origin$ = $P$

⇒ $\sqrt{(x-0)^{2} + (y-0)^{2} } = P$

⇒ $x^{2} + y^{2} = P^{2}$

∴ The locus of the point of intersection of perpendicular straight lines which are at constant distance '$P$' from the origin is $x^{2} + y^{2} = P^{2}$