Page 83 - Mathematics Class - XI

Viva-Voce

1. What is directrix in ellipse?
Ans. In case of ellipse, directrices (plural of directrix) are two parallel lines on the outside of an ellipse
perpendicular to the major axis.
If an ellipse has centre (0, 0), eccentricity (e) and semi-major axis (a) in the x-direction, then its foci are at
a
(± ae, 0) and its directrices are x = ± .
e

2. What is the equation of major axis of x 2 + y 2 = 1?
a 2 b 2
Ans. y = 0.
x 2 y 2
3. What is the equation of minor axis of + = 1?
b 2 a 2
Ans. y = 0.

4. What is the length of latus rectum of an ellipse?
x 2 y 2 2b 2
Ans. Length of latus rectum of the ellipse + = 1 is .
a 2 b 2 a
5. What is the equation of an ellipse if centre is at (h, k) instead of (0, 0)?

(xh− ) 2 (yk− ) 2
Ans. Equation of ellipse with centre (h, k) is + = 1.
a 2 b 2

MCQs

1. The eccentricity of an ellipse is
a) 1 b) 0 c) between 0 and 1 d) greater than 1

2. The distance between the foci of an ellipse is
a) 2a b) 2b c) c d) 2c
3. The standard form of the equation of an ellipse is
(xh ) 2 (yk ) 2
a) (x – h) + (y – k) = r b) 1
2
2
2
a 2 b 2
c) x 2 y 2 1 d) (y – k ) = m (x –h)
a 2 b 2
4. The foci of an ellipse are located at
a) vertices b) centre c) directrix d) none of these

5. The length of the major axis of an ellipse is given by
a) 2a b) 2b c) a + b d) 2c
6. The length of the minor axis of an ellipse is given by
a) 2a b) 2b c) a + b d) 2c

(xh ) 2 (yk ) 2
Answers: 1. c) between 0 and 1 2. d) 2c 3. b) 1
a 2 b 2
4. d) none of these 5. a) 2a 6. b) 2b
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