How do you find the coordinates of the center, foci, the length of the major and minor axis given #27x^2+9y^2=81#?

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Answer 1 · 2018-04-19T13:00:18

Center is at #(0,0)# , major axis length is #6# unit , minor axis length is # 2 sqrt3# unit , focii at # (0, -sqrt6 ), (0, sqrt6)#

#27 x ^2+9 y^2= 81 or (27 x ^2)/81+ (9 y^2)/81= 1 # or

#x ^2/3+ y^2/9= 1 or x ^2/ sqrt3^2+ y^2/3^2= 1 ; 3 > sqrt 3 #

This is standard equation of vertical ellipse with center at origin

#(0,0) ; x^2/b^2+y^2/a^2=1 ; b = sqrt 3 ; a=3 # . Major axis

length is #2 a= 6 # , Minor axis length is #2 b = 2 sqrt3#

#c^2= a^2-b^2= 9- 3 = 6 :. c= +- sqrt6#

Focii at # (0, -sqrt6 ), (0, sqrt6)#

graph{27x^2+9y^2=81 [-10, 10, -5, 5]}