We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
+1
41
3
avatar+67 

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.

 May 7, 2019
 #1
avatar+100519 
+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

 

 

 

cool cool cool

 May 7, 2019
 #3
avatar+67 
0

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.

 May 13, 2019

4 Online Users