Question

An ellipse has a vertex at (4,0), a co-vertex at (0,3), and a center at the origin. Which is the equation of the ellipse in standard form?

Answer 1

ANSWER

$\frac{ {x}^{2} }{ 16} + \frac{ {y}^{2} }{ 9} = 1$

EXPLANATION

The given ellipse has a vertex at (4,0), a co-vertex at (0,3), and a center at the origin.

The equation of an ellipse with vertices on the x-axis and center at the origin is:

$\frac{ {x}^{2} }{ {a}^{2} } + \frac{ {y}^{2} }{ {b}^{2} } = 1$

The ellipse has vertex at (4,0) , hence a=4.

Also the co-vertex is at (0,3) , b=3

We substitute the values into the equation to get:

$\frac{ {x}^{2} }{ {4}^{2} } + \frac{ {y}^{2} }{ {3}^{2} } = 1$

$\frac{ {x}^{2} }{ 16} + \frac{ {y}^{2} }{ 9} = 1$