A certain ellipse is tangent to both the \(x\)-axis and the \(y\)-axis, and its foci are at \((2, -3 + \sqrt{5})\) and \((2, -3 - \sqrt{5})\) Find the length of the major axis.

FlyEaglesFly May 7, 2019

#1**+1 **

The major axis will lie parallel to the y axis

So we have this form : (y - k)^2 + (x - h)^2

_______ _______ = 1

a^2 b^2

The center of the ellipse is (2, - 3) = (h, k)

Since the ellipse is tangent to the y axis and (2, -3) is the center.....then the minor axis must be 4 units in length

So b = 4/2 = 2 and b^2 = 2

And we can find "a" thusly : a^2 - b^2 = c^2

a^2 = ???

b^2 = 4

c^2 = (√5)^2 = 5

So

a^2 - 4 = 5

a^2 = 9

a = 3

And the major axis = 2a = 2(3) = 6

Here's a graph : https://www.desmos.com/calculator/iagepa6zop

CPhill May 7, 2019

#3**-1 **

Thanks only thing what "thusly" is that a math term I should know or is it just like a therefore. I know it is a dumb question I should know the answer to.

FlyEaglesFly May 13, 2019