Write the equation for the ellipse with a vertex at (-6,0) and a focus at (3√3,0).

Question

Write the equation for the ellipse with a vertex at (-6,0) and a focus at (3√3,0). Solve this please.

Answer 1

Typically the equation of an ellipse is (x²/a²) + (y²/b²) = 1 where the vertices are (±a,0).

In this case that would make a=6.

 

The foci are (±ae,0) where e is the eccenticity = sqrt(a² - b²)/a

In this case 6e = 3√3 => e = (1/2)√3

Therefore,

                 (1/2)√3 = sqrt(36 - b²)/6  => 3/4 = (36 - b²)/36  => 27 = 36 - b²  => b =3

 

Since you now have a and b, you know the equation for the ellipse which I gave you to start out.