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Consider the ellipse \(9(x-1)^2 + y^2 = 36\). Let A be one of the endpoints of its major axis, and let B be one of the endpoints of its minor axis. Find the distance AB.

 May 9, 2019
 #1
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9(x - 1)^2 +  y^2  = 36      divide both sides by 36

 

(x - 1)^2          y^2

______   +      ____     =  1

    4                   36

 

The center is  ( 1, 0)

The major axis is along y   and the minor along x

 

One of the enpoints on the major axis is  (1, 0 + 6)   =  ( 1, 6)

One of the points on the minoraxis is (1 + 2, 0)  =  (3, 0)

 

So the distance between these points is   sqrt [ ( 3 - 1)^2 + ( 6 - 0)^2 ]  =  sqrt [ 2^2 + 6^2 ]  =

 

sqrt [40]  =

 

2sqrt(10)  units

 

Here's a graph :  https://www.desmos.com/calculator/2zr89eh7yu

 

 

cool cool cool

 May 9, 2019

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