How do you write an equation of an ellipse in standard form given Length of major axis: 66, Vertices on the x-axis, Passes through the point (16.5 ,12 )?

1 Answer
Jul 28, 2016

Answer:

#x^2/33^2+(3y^2)/24^2=1#

Explanation:

Let the half of length of major axis be a half of length of minor axis be b.

Given the length of major axis=66

So #2a=66=>a=33#

It is also given that the vertices are on x-axis.Let the coordinate of the center of ellipse be (c,0). Then the equation of ellipse may be written as.

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

The equation can be found out,if we consider c=0
So the equation becomes

#x^2/a^2+y^2/b^2=1....(1)#

Now a=33 and the equation passes through (16.5,12).So

#(16.5)^2/33^2+12^2/b^2=1#

#=>1/4+12^2/b^2=1#

#=>12^2/b^2=1-14=3/4#

#:.b^2=12^2*4/3=24^2/3#

Putting the values of #a^2 and b^2# in equation (1) we get

#x^2/33^2+(3y^2)/24^2=1#