Q. 35.0( 1 Vote )

# Find the (i) leng

Answer : Given:

16x2 + 25y2 = 400

Divide by 400 to both the sides, we get  …(i) Since, 25 > 4

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

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

a2 = 25 and b2 = 4

a = √25 and b = √4

a = 5 and b = 2

(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 × 5

= 10 units

(ii) To find: Coordinates of the Vertices

Clearly, a > b

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

= (5, 0) and (-5, 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

= 25 – 4

c2 = 21

c = √21 …(I)

Coordinates of foci = (±√21, 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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