Question

An ellipse has a vertex at (0, -7), a co-vertex at (4,0), and a center at the origin. Which is the equation of the ellipse in standard form?

Answer 1

`\frac{ {y}^(2) }{49} + \frac{ {x}^(2) }{ 16 } = 1`

Step-by-step explanation

The given ellipse has a vertex at (0, -7), a co-vertex at (4,0), and a center at the origin.

The equation of an ellipse with vertex on the y-axis and center at the origin is given by

`\frac{ {y}^(2) }{a ^(2) } + \frac{ {x}^(2) }{ {b}^(2) } = 1`

`\frac{ {y}^(2) }{( - 7) ^(2) } + \frac{ {x}^(2) }{ {4}^(2) } = 1`

`\frac{ {y}^(2) }{49} + \frac{ {x}^(2) }{ 16 } = 1`