Question

A conci with an eccentricity of 0.6 and a directrix y = 5. What is the focus of this conic section?

A) (-3, 5)
B) (0, 5.6)
C) (0, 4.4)
D) (3, 5)

Answer 1

The focus of the conic section is (0, 3).

Step-by-step explanation:

The focus of a conic section can be found using the formula:

focus = (0, p)

where p is the distance between the vertex and the focus, given by:

p = e * d

where e is the eccentricity and d is the distance between the directrix and the vertex.

In this case, the eccentricity is 0.6 and the directrix is y = 5. So the distance between the directrix and the vertex is 5.

Therefore, the focus is:

focus = (0, 0.6 * 5) = (0, 3)