Question

the sum of the distances of p(x) from (0 -3) and (0 3) is equal to 10.

Answer 1

http://www.purplemath.com/modules/ellipse.htm

if the distances from the two foci are constant, then it is an ellipse, center at 0,0, Consider the point on the x axis x=5, the sum of distances to the foci is 10, so a=5, c=3, and b=sqrt(a^2-c^2)=4, so now you have all the parameters for the standard equation.