Respuesta :
The values of a, b, h, and k, given the equation below;
[tex]\rm \dfrac{(x-h)^2}{b^2}+\dfrac{(x-k)^2}{a^2}=1\\\\ \dfrac{(x-0)^2}{3^2}+ \dfrac{(x-3)^2}{5^2}=1[/tex]
Given
An ellipse has vertices along the major axis at (0, 8) and (0, –2).
The foci of the ellipse are located at (0, 7) and (0, –1).
Ellipse
It can be seen that the major axis is parallel to the y axis.
The major axis points are;
(h, k +a) = (0, 8)
(h, k -a) = (0, -2)
Here, k + a = 8
k - a = -2
Subtracting the equations;
k + a - k + a = 8 + 2
2a = 10
a = 10/2 = 5
The foci are;
(h, k +c) = (0, 7)
(h, k -c) = (0, -1)
Here, k + c = 7
k - c = -1
Subtracting the equations;
k + c -k + c = 7+ 1
2c = 8
c = 8/2 = 4
The foci are given by;
[tex]\rm c^2=a^2-b^2\\\\b=\sqrt{a^2-c^2} \\\\b = \sqrt{5^2-4^2}\\\\b = \sqrt{25-16} \\\\ b =\sqrt{9}\\\\ b=3[/tex]
The equation is;
[tex]\rm \dfrac{(x-h)^2}{b^2}+\dfrac{(x-k)^2}{a^2}=1\\\\ \dfrac{(x-0)^2}{3^2}+ \dfrac{(x-3)^2}{5^2}=1[/tex]
To know more about ellipse click the link given below.
https://brainly.com/question/10153896
