Question

Question 12 Find the equation for the ellipse that satisfies the given conditions: Vertices (±6, 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 , where c² = a² - b² .

Here ,
Foci( ±4, 0) = ( ±c, 0)
hence, c = 4
vertices ( ± 6, 0) = ( ± a, 0)
hence, a = 6

now, c² = a² - b²
4² = 6² - b² => 16 = 36 - b²
16 - 36 = - b² => b² = 20

now, equation of ellipse is
x²/a² + y²/b² = 1
put the values of a² = 36 { ∵a = 6 } and b² = 20.
x²/36 + y²/20 = 1

Answer 2

Hii friend,

Focus (+_c,0)= (+_4,0)

focus (c)=4

vertices (+_a,0=(+_6,0)

vertices (a)=6

C²=a²-b².

b²=a²-c²

b²=36-16
b²=20

The equation of ellipse isx²/a²+y²/b²=1

=x²/36+y²/20=1

Hope this helps you a little!!!