Asked by Isaiah Estilien on Apr 23, 2024

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Identify the vertices and co-vertices of the ellipse x249+y24=1\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 4 } = 149x2+4y2=1 .

A) vertices: (−7,0) ,(7,0) ( - 7,0 ) , ( 7,0 ) (7,0) ,(7,0) co-vertices: (0,−2) ,(0,2) ( 0 , - 2 ) , ( 0,2 ) (0,2) ,(0,2)
B) vertices: (−49,0) ,(49,0) ( - 49,0 ) , ( 49,0 ) (49,0) ,(49,0) co-vertices: (0,−4) ,(0,4) ( 0 , - 4 ) , ( 0,4 ) (0,4) ,(0,4)
C) vertices: (−2,0) ,(2,0) ( - 2,0 ) , ( 2,0 ) (2,0) ,(2,0) co-vertices: (0,−7) ,(0,7) ( 0 , - 7 ) , ( 0,7 ) (0,7) ,(0,7)
D) vertices: (0,−49) ,(0,49) ( 0 , - 49 ) , ( 0,49 ) (0,49) ,(0,49) co-vertices: (−4,0) ,(4,0) ( - 4,0 ) , ( 4,0 ) (4,0) ,(4,0)
E) vertices: (0,−2) ,(0,2) ( 0 , - 2 ) , ( 0,2 ) (0,2) ,(0,2) co-vertices: (−7,0) ,(7,0) ( - 7,0 ) , ( 7,0 ) (7,0) ,(7,0)

Vertices

Vertices refer to the corners or points where two or more edges, lines, or sides meet in geometric shapes or graphs.

Co-vertices

In an ellipse, co-vertices are the endpoints of the minor axis, perpendicular to the major axis.

  • Uncover the vertices, foci, and nucleus of ellipses and hyperbolas.
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AP
Angela Pazia Edith4 days ago
Final Answer :
A
Explanation :
The standard form of the equation of an ellipse is $\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1$, where $(h,k)$ is the center of the ellipse, $a$ is the semi-major axis (half the length of the major axis), and $b$ is the semi-minor axis (half the length of the minor axis). Comparing this to $\frac{x^2}{49}+\frac{y^2}{4}=1$, we can see that $h=k=0$, $a=7$, and $b=2$. The vertices are located at $(\pm a,0)=(\pm 7,0)$ and the co-vertices are located at $(0,\pm b)=(0,\pm 2)$, giving us the answer choice of $\boxed{\textbf{(A)}}$.