Find the equation to the locus of a point which moves so that the sum of its distances from (3,0) and (-3,0) is less than 9.

Explanation

Let `P(x,y)` be the point which moves such that sum of its distances from `F(3,0)` and `F' (−3,0)` is `9`.

The curve traced by `P` is an ellipse length of whose major axis `(2a=9)` and whose central is at the mid point of `FF'` at `(0,0)` where F, F' are the foci.

The major axis is the x-axis since the foci lie on it.

`CF=ae=3`

`a=frac{9}{2}`

` e=frac{3}{a}=frac{2}{3}`

`b=a sqrt(1-e^2)`

`b=frac{3 sqrt(5)}{2}`
...