Questions: What is the center of the ellipse defined by the equation x^2/4 + y^2/25 = 1?

Transcript text: What is the center of the ellipse defined by the equation $\frac{x^{2}}{4}+\frac{y^{2}}{25}=1$ ?

Solution

Solution Steps

Step 1: Identify the standard form of the ellipse equation

The given equation is $\frac{x^{2}}{4} + \frac{y^{2}}{25} = 1$. This is in the standard form of an ellipse equation: \[ \frac{(x-h)^{2}}{a^{2}} + \frac{(y-k)^{2}}{b^{2}} = 1, \] where $(h, k)$ is the center of the ellipse.

Step 2: Compare the given equation with the standard form

In the given equation, $h = 0$ and $k = 0$ because there are no $(x-h)$ or $(y-k)$ terms. The denominators $a^{2} = 4$ and $b^{2} = 25$ correspond to the semi-major and semi-minor axes, but they do not affect the center.

Step 3: Determine the center of the ellipse

Since $h = 0$ and $k = 0$, the center of the ellipse is at the point $(0, 0)$.