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

Question

Quizplus · Accepted Answer

To find the intercepts, rewrite the equation in standard form: $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$, where $3136 = 16x^2 + 49y^2$. Dividing by 3136 gives $\frac{x^2}{196} + \frac{y^2}{64} = 1$. Thus, $a^2 = 196$ and $b^2 = 64$, leading to $a = 14$ and $b = 8$, which matches the intercepts in option A.

Match the Equation of the Ellipse with the Appropriate Description 16x2+49y2=313616 x ^ { 2 } + 49 y ^ { 2 } = 313616x2+49y2=3136

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