Question

Which is the equation of an ellipse centered at the origin with vertices (8,0) and (-8,0) and a minor axis length of 8?

Answer 1

Answer:

OptionB is right

Step-by-step explanation:

Given that an ellipse centered at the origin with vertices (8,0) and (-8,0) and a minor axis length of 8

Since centre is at the origin, its equation would be of the form

$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

Since vertices are (8,0) and (-8,0) we find that a=8

Minor axis length = 2b =8 (given)

So b =4

The equation of the ellipse would be

$\frac{x^2}{8^2}+\frac{y^2}{4^2}=1\\\frac{x^2}{64}+\frac{y^2}{16}=1$

Option B is the right answer

Answer 2

The standard form of an ellipse with horizontal major axis as in this problem is:
$\frac{ x^{2} }{ a^{2} } + \frac{ y^{2} }{ b^{2} } =1$ where 
"a" is greater than "b"

the major axis is length of 16 which means  a = 8 and the minor axis length is 8 which means b = 4

the equation then is:   Choice B