Question

Question 1 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^2/36 + y^2/16 = 1

Class X1 - Maths -Conic Sections Page 255

Answer 1

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

Here, x²/36 + y²/16 = 1 or, x²/6² + y²/4² = 1
∵ the denominator of x²/36 is greater than denominator of y²/16 .
∴ major axis is along X - axis.

on comparing given equation with equation x²/a² + y²/b² = 1 , we get .
a = 6 and b = 4
now, c² = a² - b² = 6² - 4² = 36 - 16 = 20
c = √20

so, vertices ( ±a , 0) = ( ± 6, 0)
Foci ( ±c, 0) = ( ± √20, 0)
length of major axis = 2a = 2 × 6 = 12
length of minor axis = 2b = 2 × 4 = 8
eccentricity ( e ) = c/a = √20/6 = 2√5/6 = √5/3
length of latusrectum = 2b²/a = 2 × 16/6 = 16/3