Question

Question 3 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^2/16 + y^2/9 = 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, x²/16 +y²/9 = 1 or, x²/4² + y²/3² = 1
∵ the denominator of x²/16 is greater than denominator of y²/9 .
∴ major axis is along X - axis .

on comparing given equation with x²/a² + y²/b² = 1 we get ,
a = 4 and b = 3
now, c² = a² - b² = 4² - 3² = 16 - 9 = 7
c = √7

so, vertices ( ±a, 0) = ( ±4 , 0)
Foci ( ± c ,0) = ( ± √7, 0)
length of major axis = 2a = 2 × 4 = 8
length of minor axis = 2b = 2 × 3 = 6
eccentricity ( e ) = c/a = √7/4
length of latusrectum = 2b²/a = 2 × 9/4 = 9/2

Answer 2

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