What is an equation in standard form of an ellipse centered at the origin with vertex (-5, 0) and co-vertex (0, 3)?
The standard form of an ellipse centered at the origin is:
x^2/a^2 + y^2/b^2 = 1
where a is the distance from the center to the vertices along the x-axis, and b is the distance from the center to the co-vertices along the y-axis.
In this case, we are given that the ellipse is centered at the origin and has a vertex at (-5,0) and a co-vertex at (0,3). This tells us:
a = 5 (because the x-coordinate of the vertex is 5 units away from the origin)
b = 3 (because the y-coordinate of the co-vertex is 3 units away from the origin)
Plugging these values into the standard form equation, we get:
x^2/5^2 + y^2/3^2 = 1
Simplifying:
x^2/25 + y^2/9 = 1
Therefore, the equation in standard form of the ellipse centered at the origin with vertex (-5, 0) and co-vertex (0, 3) is x^2/25 + y^2/9 = 1.