Question

find the equation of ellipse with centre at origin and axis being the co-ordinate axis if the length of minor axis and distance between the foci and equal to 10

Answer 1

Find the equation of the ellipse referred to its centre whose minor axis is equal to the distance between the foci and whose latus is 10?

Answer:

Let the equation of the ellipse is x2a2+y2b2=1a>b

Then the foci are S(ae,0) and S′(−ae,0)

Length of minor axes =2b

Length of latus rectum =2b2a

According to the question

BB′=SS′

2b=2ae

b=ae

2b2a=10

b2=5a

b2=a2(1−e2)

a2e2=a2(1−e2)

e=12–√

b=a2–√

b2=a22

5a=a22

a=10

b2=5×10=50

Hence equation of ellipse

x2100+y250=1

Hope it helps!