Write an equation in standard form of an ellipse that is 50 units high and 40 units wide. The center of the ellipse is (0, 0)

1 answer

The standard form equation of an ellipse is $\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1$, where $(0,0)$ represents the center of the ellipse and $a$ and $b$ represent the lengths of half of the major and minor axes respectively.

In this case, the ellipse has a height of 50 units, so $a = \dfrac{50}{2} = 25$. The ellipse has a width of 40 units, so $b = \dfrac{40}{2} = 20$.

Substituting these values into the standard form equation, we have $\dfrac{x^2}{25^2} + \dfrac{y^2}{20^2} = 1$.

Simplifying, we get $\dfrac{x^2}{625} + \dfrac{y^2}{400} = 1$.

Therefore, the equation in standard form of the given ellipse is $\boxed{\dfrac{x^2}{625} + \dfrac{y^2}{400} = 1}$.