Question

Question 11 Find the equation for the ellipse that satisfies the given conditions: Vertices (0, ±13), foci (0, ±5)

Class X1 - Maths -Conic Sections Page 255

Answer 1

Concept : if foci ( 0, ± c ) and vertices ( 0, ± a) then, equation of ellipse will be of the form
x²/b² + y²/a² = 1 where, c² = a² - b² .

Here,
Foci( 0, ± c) = (0, ± 5)
hence, c = 5
vertices (0, ± 13) = ( 0, ± a)
hence, a = 13

now, c² = a² - b²
5² = 13² - b² => 25 = 169 - b²
25 - 169 = - b² => - 144 = - b²
b² = 144

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

Answer 2

Hii friend,

according to ellipse,

Foci (0,+-c)= (0,+-5)

c= 5

vertices= (0,+_a)

a= 13

c²=a²-b²

b²= 169-25

b²=144

It is a horizontal type ellipse concept. so,

Equation of ellipse= x²/b²+y²/a²=1

= x²/144+y²/169=1

hope this helps you a little!!!