Question

Which of the following is one of the foci of the conic section with the equation?

1) (0, 2√5)
2) (2√3, 0)
3) (2√5, 0)

Answer 1

In a conic section, the foci are two special points inside the curve. Comparing the equation of the conic section with the given options, we can determine that option 3, (2√5, 0), is one of the foci.

Step-by-step explanation:

In a conic section, the foci are two special points inside the curve. The sum of the distances from any point on the curve to the two foci is always constant. To determine which of the given options is one of the foci, we can look at the coordinates and compare them with the equation of the conic section.

The equation of an ellipse is usually in the form (x-h)^2/a^2 + (y-k)^2/b^2 = 1, where (h,k) is the center and a and b are the semi-major and semi-minor axes, respectively.

Comparing the equation of the conic section with the given options, we can see that option 3, (2√5, 0), matches the x-coordinate and is therefore one of the foci.