An ellipse is represented by the equation . each directrix of this ellipse is a ________________________ from the center on the

Question

1 year ago

13

major axis.

1 answer:

Anastasy [175] · Answer 1 · 2023-05-06T01:24:55+03:00

The true statement about the directrix is that each directrix of this ellipse is 31.25 units from the center on the major axis.

<h3>How to determine the distance of the directrix?</h3>

The equation of the ellipse is given as:

$\frac{(x - 5)^2}{625} -\frac{(y - 4)^2}{225} =1$

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.