Match the equation of the ellipse with the appropriate description.
-$$49 x ^ { 2 } = 3136 - 16 y ^ { 2 }$$
A) $x$-intercepts $( 64,0 ) , ( - 64,0 )$; y-intercepts $( 0,196 ) , ( 0 , - 196 )$
B) $x$-intercepts $( 8,0 ) , ( - 8,0 )$; y-intercepts $( 0,56 ) , ( 0 , - 56 )$
C) x-intercepts $( 8,0 ) , ( - 8,0 ) ; y$-intercepts $( 0,14 ) , ( 0 , - 14 )$
D) x-intercepts $\left( \frac { 7 } { 4 } , 0 \right) , \left( - \frac { 7 } { 4 } , 0 \right) ; y$-intercepts $( 0,14 ) , ( 0 , - 14 )$

Question

Quizplus · Accepted Answer

To find the intercepts, first, rewrite the equation in standard form for an ellipse. Divide everything by 3136 to get $\frac{49x^2}{3136} + \frac{16y^2}{3136} = 1$, which simplifies to $\frac{x^2}{64} + \frac{y^2}{196} = 1$. For x-intercepts, set $y=0$, which gives $x = \pm 8$. For y-intercepts, set $x=0$, which gives $y = \pm 14$.

Match the Equation of the Ellipse with the Appropriate Description 49x2=3136−16y249 x ^ { 2 } = 3136 - 16 y ^ { 2 }49x2=3136−16y2

Match the Equation of the Ellipse with the Appropriate Description $49 x ^ { 2 } = 3136 - 16 y ^ { 2 }$