Match the equation of the ellipse with the appropriate description.
-$$36 x ^ { 2 } = 2916 - 9 y ^ { 2 }$$
A) $x$-intercepts $( 2,0 ) , ( - 2,0 )$; y-intercepts $( 0,18 ) , ( 0 , - 18 )$
B) $x$-intercepts $( 81,0 ) , ( - 81,0 )$; y-intercepts $( 0,324 ) , ( 0 , - 324 )$
C) $x$-intercepts $( 9,0 ) , ( - 9,0 ) ; y$-intercepts $( 0,54 ) , ( 0 , - 54 )$
D) x-intercepts $( 9,0 ) , ( - 9,0 ) ; y$-intercepts $( 0,18 ) , ( 0 , - 18 )$

Question

Quizplus · Accepted Answer

To find the intercepts, first, rewrite the equation in standard form for an ellipse: $\frac{x^2}{81} + \frac{y^2}{324} = 1$. The square roots of the denominators give the radii: $x$-radius = 9 and $y$-radius = 18, leading to the intercepts given in option D.

Match the Equation of the Ellipse with the Appropriate Description 36x2=2916−9y236 x ^ { 2 } = 2916 - 9 y ^ { 2 }36x2=2916−9y2

Match the Equation of the Ellipse with the Appropriate Description $36 x ^ { 2 } = 2916 - 9 y ^ { 2 }$