How do you write an equation of an ellipse in standard form given vertices (6, 0), (-6, 0) and co-vertices (0, 2), (0, -2)?

1 Answer
Oct 26, 2017

Answer:

The equation of the ellipse is # x^2+9y^2=36#

Explanation:

Vertices of the Major axis of ellipse are #(a,0) , (-a,0) #

or #(6,0) , (-6,0) # and vertices of the Minor axis of ellipse are

#(0,b) , (0,-b) # or #(0,2) , (0,-2) #

Equation of an ellipse with its major axis on the x-axis and minor

axis on the y-axis is: #x^2/a^2 + y^2/b^2 = 1 ; a and b# are the length

of semi major axis and semi minor axis. Here major axis is

#2a=6+6=12 :. a=6# and minor axis is

#2b=2+2=4 :. b=2#. Hence the equation of the ellipse is

#x^2/6^2 + y^2/2^2 = 1 or x^2/36 + y^2/4 = 1 or x^2+9y^2=36# [Ans]