Question

Question 2 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^2/4 + y^2/25 = 1

Class X1 - Maths -Conic Sections Page 255

Answer 1

concept : if equation of ellipse is x²/b² + y²/a² = 1 ( b < a ) then,
vertices ( 0, ± a)
foci ( 0, ± c ) where, c² = a² - b²
Length of minor axis = 2b
length of major axis = 2a
eccentricity ( e ) = c/a
length of latusrectum = 2b²/a

Here, x²/4 + y²/25 =1 or, x²/2² + y²/5² = 1
on comparing given equation with equation x²/b² + y²/a² = 1
a = 5 and b = 2
now,c² = a² - b²
c² = 5² - 2² = 25 - 4 = 21
c = √21

so, vertices ( 0, ± a) = ( 0, ± 5)
foci ( 0, ± c) = ( 0, ± √21)
Length of major axis = 2a = 2 × 5 = 10
length of minor axis = 2b = 2 × 2 = 4
eccentricity ( e ) = c/a = √21/5
length of latusrectum = 2b²/a = 2 × 4/5 = 8/5