Question

An ellipse having foci at ( 3, 1 ) and ( 1, 1 ) passes through the point ( 1, 3) . Its eccentricity is______

Answer 1

Answer:

Step-by-step explanation:

e = 0.4142

Step-by-step explanation:

It is known that the sum of distance between a point on the ellipse and its focii is equal to 2 x a, where a is the length of the semi-major axis.  

Now, distance between the two foci is 2 x a x e = 2 units.  

And, the sum of the distance (S) between the foci and the point on the ellipse is:

S = 2 + (8)^(0.5)

Hence, we calculate e from the above two equations to be 0.4142.

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