Match the equation of the ellipse with the appropriate description.
-$$4 x ^ { 2 } + 25 y ^ { 2 } = 2500$$

Question

Quizplus · Accepted Answer

To find the intercepts, we first rewrite the equation in standard form by dividing both sides by 2500: $\frac{x^2}{625} + \frac{y^2}{100} = 1$. The square roots of the denominators give the lengths of the semi-axes: $\sqrt{625} = 25$ for $x$ and $\sqrt{100} = 10$ for $y$. Thus, the $x$-intercepts are $(\pm25, 0)$ and the $y$-intercepts are $(0, \pm10)$, matching option A.

Match the Equation of the Ellipse with the Appropriate Description 4x2+25y2=25004 x ^ { 2 } + 25 y ^ { 2 } = 25004x2+25y2=2500

Match the Equation of the Ellipse with the Appropriate Description $4 x ^ { 2 } + 25 y ^ { 2 } = 2500$