Question

find the locus of a point which is at a distance of 5 units from (2,–3)

Answer 1

Here is your answer!
Have fun with it.

Answer 2

The locus of the point is x^2-4x+y^2+6y-12=0

Let the locus of the point (x,y) be L

Now, root[ (x-2)^2 +(y+3)^2]=5

(x-2)^2 + (y+3)^2=25

x^2-4x+y^2+6y=25-13=12

Hence, the locus is x^2-4x+y^2+6y-12=0