A point moves in a manner that the sum of the squares of its distance from thr origin and the point (2,-3) is always 19.show that the locus of moving point is a circle.find the equation to the circle?
Let the variable point be
It is given that,
Using the distance formula, we have,
Rewriting after completing squares,
This exhibits that the locus of the point is a circle having
It may be interesting to note that the centre of the circle is the