What is an equation in standard form of an ellipse centered at the origin with a vertex (-6,0) and co-vertex (0,4)?

Answer 1

The standard form of an equation of an ellipse centered at the origin is:
\[ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \]
where a is the length of the semi-major axis and b is the length of the semi-minor axis.

Given that the vertex (-6, 0) and co-vertex (0, 4), we can see that the semi-major axis is 6 units long, and the semi-minor axis is 4 units long.

Therefore, the equation in standard form of the ellipse is:
\[ \frac{x^2}{6^2} + \frac{y^2}{4^2} = 1 \]
which simplifies to:
\[ \frac{x^2}{36} + \frac{y^2}{16} = 1 \]

Thus, the equation in standard form of the ellipse centered at the origin with a vertex (-6,0) and co-vertex (0,4) is:
\[ \frac{x^2}{36} + \frac{y^2}{16} = 1 \]