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  
 
0
91
1
avatar

An ellipse with equation \(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\) contains the circles \((x - 1)^2 + y^2 = 1\) and \((x + 1)^2 +y^2 = 1.\) Then the smallest possible area of the ellipse can be expressed in the form \(k \pi.\) Find \(k.\)

 Apr 5, 2019
 #1
avatar+103973 
0

The center of the ellipse will be the origin

 

The length of the major axis is 4....so a is 1/2 of this = 2 

The length of the minor axis = 2sqrt(2)....so.....b is 1/2 of this = sqrt(2)

 

So....the equation of the ellipse is

 

x^2            y^2

___    +      _________         =    1

 2^2            [sqrt(2)]^2

 

 

x^2          y^2

___ +   _____    =     1

  4            2

 

The area of the ellipse   =  pi * a * b  =  pi * 2 * sqrt(2)  =   2sqrt(2) pi

 

So

 

k  =  2sqrt (2)

 

Here is the graph : https://www.desmos.com/calculator/ovso9le6pj

 

 

 

cool cool cool

 Apr 5, 2019

10 Online Users

avatar