Question

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin.

Vertices: (+3, 0); foci: (2,0)

Answer 1

The equation of the ellipse is
`(x^(2))/(9) + (y^(2))/(5) = 1`

Explanation:

Let the equation of the ellipse is
`(x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1` {As the center of the ellipse is at the origin}

Therefore, the vertices of the ellipse are (± a,0) and foci are (± ae,0)

Now, given that a = 3 and ae = 2

Now, eccentricity of a ellipse is given by b² = a² - a²e² = 3² - 2² = 5

Therefore, the equation of the ellipse is
`(x^(2))/(9) + (y^(2))/(5) = 1` (Answer)