Find the coordinates of the foci,the vertices, the length of the major axis the minor axis, the ecentricity and the length of the latus rectum of the ellipse of 4x2+9y2=36.
KINDLY EXPLAIN STEP-BY-STEP:
standrad eqn of ellipse is X2/a2 + Y2 / b2 = 1 compairing with above eqn. we get a = 3 and b = 2
as a>b so ellipse has x axis as major axis and length of major axis is 2a = 6 and length of mionr axis is 2b = 4
eccentricity as we know b2 =a2 (1-e2) putting values of a and b we get e = 5 / 3
so focii are (ae,0) and (-ae,0) which is (5 , 0) and (-5 , 0)
length of latus rectum = 2a /e = 18 / 5