Question

dentify the equation of the ellipse that passes through (4, 2) and has foci at (1, -1) and (1, 5)

Answer 1

Have you considered writing a FORM of an ellipse and filling in what you know?

Usually, \(\dfrac{(x-h)^{2}}{a^{2}} + \dfrac{(y-k)^{2}}{b^{2}} = 1\)

Answer 2

okay but im not sure which would resprent k or h? and a and b

Answer 3

Well, that's where we start answering questions.

Given the foci, (1, -1) and (1, 5), you can find the center and thus, h and k. The center is in the middle. Find the midpoint of the line connecting the foci and you will have the center,