equation of the ellipse is = . Example Find the equation of the ellipse, whose length of the major axis is and foci are ( , ± ). Solution Since the foci are on y -axis, the major axis is along the y -axis. So, equation of the ellipse is of the form b = .
Given that a = semi-major axis and the relation c = a – b gives = – b i.e. , b = Therefore, the equation of the ellipse is Example Find the equation of the ellipse, with major axis along the x -axis and passing through the points ( , ) and (– , ). Solution The standard form of the ellipse is b = . Since the points ( , ) and (– , ) lie on the ellipse, we have + b ...
( ) and b = ….( ) Solving equations ( ) and ( ), we find that a = and b = Hence the required equation is CONIC SECTIONS , i.e., x + y = . EXERCISE . In each of the Exercises to , find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse. .
x + y = In each of the following Exercises to , find the equation for the ellipse that satisfies the given conditions: . Vertices ( ± , ), foci ( ± , ) . Vertices ( , ± ), foci ( , ± ) . Vertices ( ± , ), foci ( ± , ) .
Ends of major axis ( ± , ),