Question

How do you use the definition of an ellipse and the distance formula to find an equation of the ellipse whose minor axis has length 12 and its focal points are at (1, 2) and (4,-2)?

Answer 1

`sqrt(((x-1)^2+(y-2)^2)) + sqrt((x-4)^2+(y+2)^2)) =\ 13`

Explanation:

The distance between focal points .= (major axis length) X (eccentricity) = 2ae = 5

Semi-minor axis length b = a`sqrt(1-e^2)` = 6.
So, a = 6.5
The sum of the distances of any point ( x, y ) on the ellipse from the focal points = 2a =13.

`sqrt(((x-1)^2+(y-2)^2)) + sqrt((x-4)^2+(y+2)^2)) =\ 13`