How do you write an equation of an ellipse in standard form given center is at origin, major axis is 18 minor axis is 6?

1 Answer
Nov 15, 2015

Answer:

#x^2/81 + y^2/9 = 1# if the major axis is horizontal
#x^2/9 + y^2/81 = 1# if the major axis is vertical

Explanation:

#C: (0, 0)#

#M = 18 = 2a => a = 9#

#m = 6 = 2b => b = 3#


If the major axis is horizontal, the standard equation of the ellipse is

#(x - h)^2/a^2 + (y - k)^2/b^2 = 1#

#=> (x - 0)^2/9^2 + (y - 0)^2/3^2 = 1#

#=> x^2/81 + y^2/9 = 1#


If the major axis is vertical, the standard equation of the ellipse is

#(x - h)^2/b^2 + (y - k)^2/a^2 = 1#

#=> (x - 0)^2/3^2 + (y - 0)^2/9^2 = 1#

#=> x^2/9 + y^2/81 = 1#