Find the equation of the locus of the center of the circle which touches the X axis, and also touches the Circle with Center(0,3) and Radius 2 units. Also prove that this locus is a Parabola.
Please help on how to start the problem.
My approach was finding 2 points which are definitily present on the locus (by rough plot) and then proving y^2 is proportional to x, but I guess that won't work.
Second approach:
Obviously the parabola in question is:
- opening upward
- symmetric to the y-axis
Therefore the genral equation of such a parabola is:
There are 2 points which lay on the parabola: and Q(5,3)
Plug in the coordinates of these points and solve the system of equations for a and b:
You'll get: