1.

Determine the foci coordinates, the vertices, the length of the major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse (x2/49) + (y2/36) = 1​

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Answer:

Solution:

The given equation is (x2/49) + (y2/36) = 1

It can be written as (x2/72) + (y2/62) = 1

It is noticed that the denominator of x2/49 is greater than the denominator of the y2/36

On comparing the equation with (x2/a2) + (y2/b2) = 1, we will get

a= 7 and b = 6

Therefore, c = √(a2– b2)

Now, substitute the value of a and b

⇒ √(a2– b2) = √(72– 62) = √(49-36)

⇒ √13

Hence, the FOCI COORDINATES are ( ± √13, 0)

Eccentricity, e = c/a = √13/ 7

Length of the major axis = 2a = 2(7) = 14

Length of the minor axis = 2b = 2(6) =12

The coordinates of the VERTICES are ( ± 7, 0)

Latus rectum Length= 2b2/a = 2(6)2/7 = 2(36)/7 = 72/7


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