Question

the elliptical equation, ^2/16 − ^2/4 = 1, the focci are located at points 16 4a. (±2√3, 0)b. (±2√5, 0) c. (0, ±3√2)d. (0, ±2√5)e. (4,2)

Answer 1

An ellipse is a generalized case of a closed conical section.

The equation of an ellipse is a generalized case of the equation of a circle. It has the following form:

`(x^2)/(a^2)+(y^2)/(b^2)=1`

The foci of a horizontal ellipse are:

`\begin{gathered} F_1=(-\sqrt[]{b^2-a^2}+c_1,c_2) \\ F_2=(\sqrt[]{b^2-a^2}+c_1,c_2) \end{gathered}`

Foci, in this case, would be:

`(0,\pm2\sqrt[]{3})`