Find the quadratic equation for the locus of points whose sum of its distance from (1, 0) and (−1, 0) is 6.
I know to start with sqrt( (x-1)^2 +y^2) + sqrt( (x+1)^2+y^2)=6, then square both sides. I'm not sure about the algebra after squaring both sides as I got that part wrong.
We have an ellipse
The focal points are (-1,0) and (1,0)
Using symmetry, the center is (0, 0)
c = the distance from the center to either foci = 1
The sum of the distances from any point on the ellipse to the focal points = 2a
2a = 6
a = 3 ⇒ a^2 = 9
b^2 = a^2 - c^2 = 9 - 1 = 8
The equation is
x^2/a^2 + y^2/b^2 = 1 .....so.....
x^2 / 9 + y^2 / 8 = 1