How do you write an equation of an ellipse in standard form given eccentricity of 0.5 if the vertices for the ellipse occur at the points ( 0 , 7 ) and ( 0, -9 )?
Given that the vertices of an ellipse are (0,7) and (0,-9).
We can say that the center of the ellipse is
and semi major axis
Now it is given that its eccentricity
Again we know
So standard equation of the ellipse having center (0,-1) and semi major axis a=8 (along y-axis) and semi minor axis