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