Question

An ellipse has a vertex at (1,0), a co-vertex at (0,4), and a center at the origin. Which is the equation of the ellipse in standard form?

x^2/16+y^2/1=1

x^2/1+y^2/4=1

x^2/4+y^2/1=1

x^2/1+y^2/16=1

Answer 1

`(x^(2) )/(1 ) +(y^(2) )/(16 ) =1`

Explanation:

The center of the ellipse at the origin, and (1,0) and (0,4) are the vertex and co-vertex of it.

Therefore, the major and minor axis of the ellipse is X-axis and Y-axis respectively.

And the standard form of the equation of ellipse is
`(x^(2) )/(a^(2) ) +(y^(2) )/(b^(2) ) =1`, where a = half of major axis length and b = half of minor axis length.

So, a = 1 and b = 4.

Therefore, the equation of the given ellipse is
`(x^(2) )/(1^(2) ) +(y^(2) )/(4^(2) ) =1`

⇒
`(x^(2) )/(1 ) +(y^(2) )/(16 ) =1` (Answer)