Identify the vertices and the foci.
-$$\frac { x ^ { 2 } } { 14 } + \frac { y ^ { 2 } } { 2 } = 1$$
A) vertices: $( 0,14 )$ and $( 0 , - 14 )$;
foci: $( 0,12 )$ and $( 0 , - 12 )$
B) vertices: $( 14,0 )$ and $( - 14,0 )$;
foci: $( 12,0 )$ and $( - 12,0 )$
C) vertices: $( 0 , \sqrt { 14 } )$ and $( 0 , - \sqrt { 14 } )$
foci: $( 0,2 \sqrt { 3 } )$ and $( 0 , - 2 \sqrt { 3 } )$
D) vertices: $( \sqrt { 14 } , 0 )$ and $( - \sqrt { 14 } , 0 )$;
foci: $( 2 \sqrt { 3 } , 0 )$ and $( - 2 \sqrt { 3 } , 0 )$

Question

Quizplus · Accepted Answer

The given equation is of an ellipse in the form $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ with $a^2 = 14$ and $b^2 = 2$. The vertices are along the major axis, which is the x-axis in this case, at $(\pm\sqrt{14}, 0)$. The foci are also along the x-axis, calculated using $c = \sqrt{a^2 - b^2} = \sqrt{14 - 2} = \sqrt{12} = 2\sqrt{3}$, giving the foci at $(\pm 2\sqrt{3}, 0)$.

Identify the Vertices and the Foci x214+y22=1\frac { x ^ { 2 } } { 14 } + \frac { y ^ { 2 } } { 2 } = 114x2​+2y2​=1

Identify the Vertices and the Foci $\frac { x ^ { 2 } } { 14 } + \frac { y ^ { 2 } } { 2 } = 1$