Question

Question 7 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 36x^2 + 4y^2 = 144

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,
36x² + 4y² = 144
36x²/144 + 4y²/144 = 144/144
x²/4 + y²/36 = 1
x²/2² + y²/6² = 1 compare this equation with above standard equation of ellipse .
we get , a = 6 and b = 2

now,c² = a² - b²
c² = 6² - 2² = 36 - 4 = 32
c = 4√2

Hence,
vertices ( 0, ± a) = ( 0, ± 6)
Foci ( 0, ± c) = ( 0, ± 4√2)
Length of minor axis = 2b = 2 × 2 = 2
Length of major axis = 2a = 2 × 6 = 12
eccentricity ( e ) = c/a = 4√2/6 = 2√2/3
Length of latusrectum = 2b²/a = 2 × 4/6 = 4/3