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.
+128473 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
