Question

Find the equation of the ellipse: Center (3, 2) a=3c, Foci: (1, 2) (5, 2)

Answer 1

The equation of an ellipse is given by:
\[(x-p)^{2}/a+(y-q)^{2}/b=1\]
(p,q) is the center of the ellipse.
a is the semi-major axis and b is the semi-minor axis.
The distance between the two foci is given by:
\[2ae\]
where e is the ellipse's eccentricity.
Find e, first.
Then :
\[e=\sqrt{1+b ^{2}/a^{2}}\]
Find b from this.
Clear?