Question

Question 15 Find the equation for the ellipse that satisfies the given conditions: Length of major axis 26, foci (±5, 0)

Class X1 - Maths -Conic Sections Page 255

Answer 1

concept : if equation of ellipse is x²/a² + y²/b² = 1 , then, foci ( ± c , 0) where, c² = a² - b² .and length of minor axis = 2a .


Here,
Length of minor axis = 2a = 26
a = 13 .
Foci ( ±5, 0) = ( ± c , 0)
hence, c = 5
now, c² = a² - b²
5² = 13² - b² => 25 = 169 - b²
b² = 169 - 25 = 144 => b² = 144

now, equation of ellipse is
x²/a² + y²/b² = 1
put the values of a² = 169 { ∵a = 13} and b² = 144
x²/169 + y²/144 = 1