The true statement about the directrix is that each directrix of this ellipse is 31.25 units from the center on the major axis.
How to determine the distance of the directrix?
The equation of the ellipse is given as:
[tex]\frac{(x - 5)^2}{625} -\frac{(y - 4)^2}{225} =1[/tex]
The above means that:
a^2 = 625
a = 25
b^2 = 225
b = 15
Calculate c using:
c^2 = a^2 - b^2
This gives
c^2 = 625 - 225
Evaluate the difference
c^2 = 400
Evaluate the square root
c = 20
The equation of the directrix is
x - x₀ = ± a²/c
So, we have:
x - x₀ = ± 625/20
Evaluate the quotient
x - x₀ = ± 31.25
This means that, each directrix is 31.25 units from the center on the major axis.
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