Question

Question 5 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^2/49 + y^2/36 = 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,
x²/49 + y²/36 = 1
x²/7² + y²/6² = 1
we observed that denominator of x²/49 is larger than the denominator of y²/36 .
hence, major axis is along X - axis .

now, after comparing given equation to standard equation of ellipse .
we get, a = 7 and b = 6
c² = a² - b² = 7² - 6² = 49 - 36 = 13
c = √13

so, vertices ( ±a, 0) = ( ±7, 0)
foci ( ±c, 0) = ( ±√13, 0)
Length of major axis = 2a = 2 × 7 = 14
Length of minor axis = 2b = 2 × 6 = 12
eccentricity ( e ) = c/a = √13/7
length of latusrectum = 2b²/a = 2 × 36/7 = 72/7