Question

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.

4x² + 9y² = 36

Answer 1

Equation of ellipse 4x² + 9y² = 36

`(4x^2)/36 + (9y^2)/36 = 1` ⇒`x^2/9 + y^2/4= 1`

The major axis is along the x-axis.

∴ a² = 9, b² = 4

∴ a= 3, b = 2

c² = a² – b² = 9 – 4 = 5

∴ c = `sqrt5`

Coordinates of foci are (± c, 0) or (±`sqrt5`, 0)

Coordinates of vertices are (± a, 0) or (± 3,0)

Length of major axis = 2a = 2 × 3 = 6

Length of minor axis = 2b = 2 × 2 = 4

Eccentricity = e = `"c"/"a"`

= `sqrt5/3`

Length of latus rectum = `(2"b")^2/"a"`

= `(2 xx 4)/3`

= `8/3`