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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