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