Question

Write an equation of an ellipse centered at the origin, satisfying the given conditions. vertex (0,\sqrt(28)); covertex (-5,0)

Answer 1

is that correct

Answer 2

The standard form equation of an ellipse centered at the origin is:
$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$
where $a$ is the distance from the center to the vertex, and $b$ is the distance from the center to the co-vertex.

Using the given information, we know that:

$a=\sqrt{28}$ (distance from center to vertex)
$b=5$ (distance from center to co-vertex)

Substituting these values into the standard form equation, we get:

$\frac{x^2}{(\sqrt{28})^2}+\frac{y^2}{5^2}=1$

Simplifying, we can write the equation as:

$\frac{x^2}{28}+\frac{y^2}{25}=1$

Therefore, the equation of the ellipse is $\frac{x^2}{28}+\frac{y^2}{25}=1$.

Answer 3

Yes, that is correct.