Respuesta :
Answer:
(a)
- The vertices are at (0,-5) and (0,5).
- The coordinates of the foci are (0,-3) and (0,3).
- Eccentricity=3/5
(b)Length of the major axis=10
Step-by-step explanation:
When the major axis of an ellipse is parallel to the y-axis.The standard form of the equation of an ellipse is given as:
[tex]\dfrac{x^2}{b^2}+\dfrac{y^2}{a^2}=1[/tex]
Given the equation:
[tex]\dfrac{x^2}{16}+\dfrac{y^2}{25}=1[/tex]
(I)The coordinates of the vertices are [tex](0, \pm a)[/tex]
[tex]a^2=25\\a^2=5^2\\a=5[/tex]
Therefore, the vertices are at (0,-5) and (0,5).
(II)The coordinates of the foci are [tex](0, \pm c)$ where c^2=a^2-b^2[/tex]
[tex]c^2=a^2-b^2\\c^2=25-16\\c^2=9\\c=3[/tex]
The coordinates of the foci are (0,-3) and (0,3).
(III)Eccentricity
This is the ratio of the distance c between the center of the ellipse and each focus to the length of the semi major axis.
Simply put, Eccentricity =c/a
Eccentricity=3/5
(b)Length of the major axis
The length of the major axis=2a
=2(5)=10.
