Question

How do you write an equation of an ellipse in standard form given foci = (0,-3) and (0,3);length of major axis: 10?

Answer 1

`x^2/25+y^2/16=1`.

Explanation:

Foci are on the major axis. So, the major axis is x-axis . Center is the midpoint of the the line joining the foci, (0, 0).
So, the equation of the ellipse is
`x^22/(a^2)+y^2/(b^2)=1`,
where a and b are the lengths of semi-major and semi-minor axes.

The eccentricity e = (distance between the foci)`/`(the length of the major axis) = (2ae)/(2a)=3/5.

The semi-minor axis b = a`sqrt(1-e^2)` = 5`sqrt(1-9/25)` = 4
Answer: `x^2/25+y^2/16=1`.