Question

the elliptical equation, ^2/16 + ^/4 = 1, the focci are located at pointsa. (±2√2, 0)b. (±2√3, 0)c. (±3√2, 0) d. (0, ±3√2) e. (4,2)

Answer 1

We have the following equation:

`(x^2)/(16)+(y^2)/(4)=1`

For this case the center is: C(0,0)

`a=\sqrt[]{16}=4,b=\sqrt[]{4}=2`

We can find the value of c like this:

`c=\sqrt[]{16-4}=\sqrt[]{12}=2\sqrt[]{3}`

Since x is the bigger axis we have the following coordinates for the focci:

`(0+2\sqrt[]{3},0),(0-2\sqrt[]{3},0)=(2\sqrt[]{3},0),(-2\sqrt[]{3},0)`

Then the answer is:

b. (±2√3, 0)