 # Ellipse

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• Q1

The equation of the ellipse with focus at (±5, 0) and x = 36/5 as one directrix is

Marks:1 ##### Explanation: • Q2

The length of the semi-latus rectum of an ellipse is one third of its major axis, its eccentricity is

Marks:1 ##### Explanation: • Q3

The eccentricity of the ellipse 25x 2 + 9y2 = 225 is

Marks:1

4/5.

##### Explanation:

The given equation is 25x2 + 9y2 = 225 x2/9 + y2/25 = 1.

Comparing with standard equation we get
a = 3, b = 5,

For ellipse,
a = b (1 - e2) 3 = 5 (1 - e2) e2 = 1 - (9/25) e = 4/5.

• Q4

The eccentricity of the ellipse 9x2 + 5y2 – 30y = 0 is

Marks:1

2/3.

##### Explanation:

The given equation can be written as

9x2 + 5(y – 3)2 = 45 (x - 0)2/5 + (y - 3)2/9 = 1

Hence, a2 = 5, b2 = 9 and the eccentricity is given by

a2 = b2 (1 – e222) 5 = 9(1– e2)

Therefore, e = 2/3.

• Q5

The eccentricity of an ellipse whose latus rectum is equal to distance between foci is

Marks:1 ##### Explanation:

The length of latus rectum of an ellipse is 2b2/a and

distance between foci is 2ae, where e is ecentricity of the ellipse.

2ae = 2b2/a  (given ) e = b2/a2

Also, we know that
e2 = 1- b2/a2 e2 = 1- e e2 + e -1 = 0 