How do you find the coordinates of the center, foci, the length of the major and minor axis given #16x^2+9y^2=144#?

1 Answer
Shwetank Mauria
Oct 29, 2016

Center is #(0,0)#, focii are #(0,sqrt7)# and #(0,-sqrt7)#, major axis is along #y#-axis and is #8#, and minor axis is along #x#-axis and is #6#.

Explanation:

Note that equation #16x^2+9y^2=144# by dividing each term by #144# can be written as #x^2/9+y^2/16=1#

As the standard equation is of the form #x^2/a^2+y^2/b^2=1#, center is #(0,0)#.

In this equation major axis is along #y#-axis and is #2b=8#, and minor axis is along #x#-axis and is #2a=6#.

As #a=3# and #b=4#, focii are given by #+-sqrt(4^2-3^2)=+-sqrt7# i.e. #(0,sqrt7)# and #(0,-sqrt7)#
graph{16x^2+9y^2=144 [-10, 10, -5, 5]}

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