Respuesta :
The directrix of the ellipse from the center of the major axis is 31.25 units. Then the correct option is D.
What is an ellipse?
Ellipse is a locus of a point that moves in a plane such that the sum of its distances from the two points called foci adds up to a constant. It is taken from the cone by cutting it at an angle.
The equation of the ellipse is given below.
[tex]\rm \dfrac{(x-5)^2}{625}+ \dfrac{(y-4)^2}{225}=1\\\\\\\dfrac{(x-5)^2}{25^2}+ \dfrac{(y-4)^2}{15^2}=1[/tex]
Then the standard equation of the ellipse will be
[tex]\rm \dfrac{(x)^2}{a^2}+ \dfrac{(y)^2}{b^2}=1[/tex]
On comparing, we have
a = 25 and b = 15
Then the eccentricity (e) of an ellipse will be
[tex]e = \sqrt{1-\dfrac{b^2}{a^2}}\\\\\\e = \sqrt{1-\dfrac{15^2}{25^2}} \\\\\\e = 0.8[/tex]
Then the directrix of the ellipse from the center of the major axis will be
[tex]\Rightarrow \dfrac{a}{e}\\\\\Rightarrow \dfrac{25}{0.8}\\\\\Rightarrow 31.25 \ units[/tex]
Thus, the directrix of the ellipse from the center of the major axis is 31.25 units.
More about the ellipse link is given below.
https://brainly.com/question/19507943
Answer:
D on edge
Step-by-step explanation:
vertical line that is 31.25 units
