Points to observer in ellipse
o Ellipse is symmetric with respect to both the coordinate axes since if ( x , y ) is a point on the ellipse , then (– x , y ), ( x , – y ) and (– x , – y ) are also points on the ellipse . o The foci always lie on the major axis . o The major axis can be determined by finding the intercepts on the axes of symmetry . That is , major axis is along the x-axis if the coefficient of x 2 has the larger denominator and it is along the y-axis if the coefficient of y 2 has the larger denominator .
Latus Rectum of Ellipse : Latus rectum of an ellipse is a line segment perpendicular to the major axis through any of the foci and whose end points lie on the ellipse . Length of Latus rectum of ellipse : 2b 2 / a
Numerical : Find the coordinates of the foci , the vertices , the length of major axis , the minor axis , the eccentricity and the latus rectum of the ellipse x 2 / 25 + y 2 / 9 = 1 Solution : Since denominator of x larger than the denominator of y , the major axis is along the x-axis . Comparing the given equation with x 2 / a 2 + y 2 / b 2 = 1 , we get a = 5 and b = 3 . Also c = √ ( a 2 – b 2 ) = √ ( 25 – 9 ) = 4