Question

Question 10 Find the equation for the ellipse that satisfies the given conditions: Vertices (±5, 0), foci (±4, 0)

Class X1 - Maths -Conic Sections Page 255

Answer 1

concept : if Foci ( ±c , 0) and vertices ( ±a, 0) then, equation of ellipse will be of the form
x²/a² + y²/b² = 1 .

Here,
Foci( ±c, 0) = ( ±4, 0)
hence, c = 4
vertices ( ±a , 0) = ( ±5, 0)
hence, a = 5

now, c² = a² - b²
4² = 5² - b² => 16 = 25 - b²
16 - 25 = -b² => b² = 9

now, equation of ellipse is
x²/a² + y²/b² = 1
put the values of a² = 25 {∵ a = 5 } and b² = 9
x²/25 + y²/9 = 1