Graph the ellipse. Specify the lengths of the major and minor axes, the foci and the eccentricity. $9 x ^ { 2 } + 16 y ^ { 2 } = 144$
A) length of major axis: 8; Length of minor axis: 6; Foci: $( 0 , \pm \sqrt { 7 } )$ ; Eccentricity: $\frac { \sqrt { 7 } } { 4 }$
B) length of major axis: 4; Length of minor axis: 3; Foci: $( 0 , \pm \sqrt { 7 } )$ ; Eccentricity: $\frac { \sqrt { 7 } } { 4 }$
C) length of major axis: 9.6; Length of minor axis: 7.2; Foci: $( 0 , \pm \sqrt { 7 } )$ ; Eccentricity: $$\frac { \sqrt { 7 } } { 4 }$$
D) length of major axis: 8; Length of minor axis: 6; Foci: $( \pm \sqrt { 7 } , 0 )$ ; Eccentricity: $\frac { \sqrt { 7 } } { 4 }$
E) length of major axis: 4; Length of minor axis: 3; Foci: $( \pm \sqrt { 7 } , 0 )$ ; Eccentricity: $\frac { \sqrt { 7 } } { 4 }$

Question

Graph the ellipse. Specify the lengths of the major and minor axes, the foci and the eccentricity. $9 x ^ { 2 } + 16 y ^ { 2 } = 144$
A) length of major axis: 8; Length of minor axis: 6; Foci: $( 0 , \pm \sqrt { 7 } )$ ; Eccentricity: $\frac { \sqrt { 7 } } { 4 }$ 
B) length of major axis: 4; Length of minor axis: 3; Foci: $( 0 , \pm \sqrt { 7 } )$ ; Eccentricity: $\frac { \sqrt { 7 } } { 4 }$ 
C) length of major axis: 9.6; Length of minor axis: 7.2; Foci: $( 0 , \pm \sqrt { 7 } )$ ; Eccentricity: $$\frac { \sqrt { 7 } } { 4 }$$ 
D) length of major axis: 8; Length of minor axis: 6; Foci: $( \pm \sqrt { 7 } , 0 )$ ; Eccentricity: $\frac { \sqrt { 7 } } { 4 }$ 
E) length of major axis: 4; Length of minor axis: 3; Foci: $( \pm \sqrt { 7 } , 0 )$ ; Eccentricity: $\frac { \sqrt { 7 } } { 4 }$

Quizplus · Accepted Answer

The equation of the ellipse is in the form $\frac{(x-0)^2}{(\sqrt{16})^2}+\frac{(y-0)^2}{(\sqrt{9})^2}=1$, which means the center of the ellipse is at the origin $(0,0)$ and the semi-axes lengths are $a=4$ and $b=3$. The length of the major axis is $2a=8$ and the length of the minor axis is $2b=6$. The foci are located at $c=\sqrt{a^2-b^2}=\sqrt{7}$ units away from the center along the major axis, which gives the foci as $(\pm\sqrt{7},0)$. Therefore, choice D is the correct answer.

Graph the Ellipse 9x2+16y2=1449 x ^ { 2 } + 16 y ^ { 2 } = 1449x2+16y2=144

Graph the Ellipse $9 x ^ { 2 } + 16 y ^ { 2 } = 144$