Question

Q12. Find the equation of the ellipse whose vertices are (+5,0) and focii are (+4,0)
nro the points 1 7 10 1.166) and (-496) the vertices of a right angled triangle.​

Answer 1

Step-by-step explanation:

Since the foci of the ellipse are F

1

(−3,0) and F

2

(3,0) which lie on the x−axis and the mid-point of the line segment

F

1

F

2

is (0,0),∴, origin is the centre of the ellipse and the major axis lies along x−axis.

Hence the equation of the ellipse can be taken as

a

2

x

2

+

b

2

y

2

=1 .........(1)

As the vertices are (±5,0).So,a=5

Also,c=3

We know that b

2 =a 2−c 2

=5

2

−3

2

=25−9=16

From equation (1), the equation of the ellipse is

25

x

2

+

16

y

2

=1