Question

please help me with this?
Find the standard form of the equatoin of the ellipse with the given characteristics.
foci: (- 7, - 3), (- 7, 1)
endpoints of the major axis (- 7, - 7), (- 7, 5)

Answer 1

So we see that the x-coordinate does not change, so that means we have the form x^2/b^2 +y^2/a^2 = 1. This also means that the coordinates of the endpoints are at y = + /- a. So I see that the distance from one endpoint to the other endpoint along the y-axis is 12, meaning a = 6. As for the foci, these points are at y = +/- c. So I also see that the distance between those foci is 4 along the y-axis, which makes my c value = 2. Given that, I can now find b. So b^2 = a^2 - c^2. So we have 36 - 4 = 32. so b^2 = 32. Given that we have this so far (x-h)^2/32 + (y-k)^2/36 = 1. Now all we need are h and k. We can easily see that x = -7, and y be in between your two foci points, meaning y will be at -1. So that means we have (x-h) = (x-(-7)) = (x+7) and (y-k) =
(y-(-1)) = (y+1). Finally we can put (x+7)^2/32 + (y+1)^2/36 = 1.
Sorry for the lengthy explanation and time wait. I still need my own review with this stuff, but what I explained is the process.