Equation of a locus- help! (1 Viewer)

[fifibum]

Hey, I know nothing about the locus..Point P(x,y) moves so that the midpoint between P and the origin
is always a point on the circle x^2 + y^2 = 1. Find the equation of the locus of P...from Maths In Focus Ex 7.2




Thanks!

 

[InteGrand]

Hey, I know nothing about the locus..Point P(x,y) moves so that the midpoint between P and the origin
is always a point on the circle x^2 + y^2 = 1. Find the equation of the locus of P...from Maths In Focus Ex 7.2




Thanks!

If the midpoint lies on the unit circle, then P must be 2 units from O. Conversely if P is 2 units from O, the midpoint lies on the unit circle.

Hence the desired locus is the circle of radius 2 centred at the origin, i.e. x²+ y²= 4.