Match the equation of the ellipse with the appropriate description.
-$$49 y ^ { 2 } = 11,025 - 9 x ^ { 2 }$$
A) $x$-intercepts $( 35,0 ) , ( - 35,0 )$; y-intercepts $( 0,15 ) , ( 0 , - 15 )$
B) $x$-intercepts $( 15,0 ) , ( - 15,0 )$; y-intercepts $( 0,35 ) , ( 0 , - 35 )$
C) $x$-intercepts $( 225,0 ) , ( - 225,0 )$; y-intercepts $( 0,1225 ) , ( 0 , - 1225 )$
D) $x$-intercepts $( 1225,0 ) , ( - 1225,0 )$; y-intercepts $( 0,225 ) , ( 0 , - 225 )$

Question

Quizplus · Accepted Answer

To find the intercepts, first rewrite the equation in standard form for an ellipse: $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$. Dividing the given equation by 11,025 gives $\frac{x^2}{1225} + \frac{y^2}{225} = 1$, where $a^2 = 1225$ and $b^2 = 225$. Thus, $a = 35$ and $b = 15$, leading to $x$-intercepts at $(\pm 35, 0)$ and $y$-intercepts at $(0, \pm 15)$.

Match the Equation of the Ellipse with the Appropriate Description 49y2=11,025−9x249 y ^ { 2 } = 11,025 - 9 x ^ { 2 }49y2=11,025−9x2

Match the Equation of the Ellipse with the Appropriate Description $49 y ^ { 2 } = 11,025 - 9 x ^ { 2 }$