Match the equation of the ellipse with the appropriate description.
-$$4 x ^ { 2 } + 25 y ^ { 2 } = 2500$$
A) $x$-intercepts $( 25,0 ) , ( - 25,0 ) ; y$-intercepts $( 0,10 ) , ( 0 , - 10 )$
B) $x$-intercepts $( 100,0 ) , ( - 100,0 )$; $y$-intercepts $( 0,625 ) , ( 0 , - 625 )$
C) x-intercepts $( 625,0 ) , ( - 625,0 ) ; y$-intercepts $( 0,100 ) , ( 0 , - 100 )$
D) $x$-intercepts $( 10,0 ) , ( - 10,0 )$; y-intercepts $( 0,25 ) , ( 0 , - 25 )$

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 $4 x ^ { 2 } + 25 y ^ { 2 } = 2500$