Question

Question 6 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^2/100 + y^2/400 = 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, x²/100 + y²/400 = 1
x²/10² + y²/20² = 1
after comparing this equation with standard equation of ellipse .
a = 20 and b = 10
now, c² = a² - b² = 20² - 10²
c² = 400 - 100 = 300
c = 10√3

so, vertices ( 0, ± a) = ( 0, ± 20)
Foci ( 0, ±c) = ( 0, ±10√3)
length of minor axis = 2b = 2 × 10 = 20
Length of major axis = 2a = 2 × 20 = 40
eccentricity ( e ) = c/a = 10√3/20 = √3/2
Length of Latusrectum = 2b²/a = 2 × 100/20=10