# Find the (i) leng Given:

x2 + 4y2 = 100

Divide by 100 to both the sides, we get  …(i) Since, 100 > 25

So, above equation is of the form, …(ii)

Comparing eq. (i) and (ii), we get

a2 = 100 and b2 = 25

a = √100 and b = √25

a = 10 and b = 5

(i) To find: Length of major axes

Clearly, a > b, therefore the major axes of the ellipse is along x axes.

Length of major axes = 2a

= 2 × 10

= 20 units

(ii) To find: Coordinates of the Vertices

Clearly, a > b

Coordinate of vertices = (a, 0) and (-a, 0)

= (10, 0) and (-10, 0)

(iii) To find: Coordinates of the foci

We know that,

Coordinates of foci = (±c, 0) where c2 = a2 – b2

So, firstly we find the value of c

c2 = a2 – b2

= 100 – 25

c2 = 75

c = √75

c = 5√3 …(I)

Coordinates of foci = (±5√3, 0)

(iv) To find: Eccentricity

We know that,  [from (I)]

(v) To find: Length of the Latus Rectum

We know that,   Rate this question :

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