Question

hey can someone help me with these 2 last questions that I have??? It's so confusing and I would really like it if someone could explain it to me as well. Thanks!

Answer 1

First find the focii of the ellipse

Focus is (c,0) where c is distance from the center of the ellipse to the focus. The other focus is at (-c, 0).

c^2 = a^2 - b^2 where a is the horizontal distance from centre to the ellipse and b is the vertical distance.

Here c^2 = 5^2 - 3^2 = 16

so c = 4

The directrices are x = = a^2 / c and - a^2/c.

So one of the directrix lines is a^2/c = 25/4 = 6.25 units from the center of the ellipse. That is at the point (9.25, 0)

On the left we calculate that the other directrix is 6.25 to the left of the center - that is at (-3.25,0)

Answer x = -3.25 and x = 9.25 are the required directrices

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