Page 80 - Mathematics Class - XI

Viva-Voce

1. State the equation of an ellipse with foci on the x-axis.
x 2 y 2
Ans. The equation of an ellipse with foci on the x-axis is + = 1
a 2 b 2
x 2 y 2
2. What is length of the latus rectum of ellipse + = 1?
a 2 b 2
2b 2
Ans. .
a
3. What is the major axis and minor axis of an ellipse?
Ans. The line segment through the foci of an ellipse is called the major axis and the line segment through the
centre and perpendicular to the major axis is called the minor axis.
4. What is the relationship between semi major axis a, semi minor axis b and the eccentricity e of an ellipse?

Ans. The relationship between semi major axis a, semi minor axis b and the eccentricity e of an ellipse is
b = a (1 – e ).
2
2
2
x 2 y 2
5. Write the length of major axis and minor axis of an ellipse + = 1.
9 4
x 2 y 2 x 2 y 2
Ans. Given, + = 1 ⇒ + = l
9 4 3 2 2 2
x 2 y 2
On comparing with + = 1, we get a = 3 and b = 2
a 2 b 2
Therefore, length of major axis = 2a = 2 × 3 = 6; length of minor axis = 2b = 2 × 2 = 4

MCQs

1. The vertices of an ellipse x 2 y 2 1
25 9
a) (0, + 50) b) ( + 5, 0) c) ( + 3, 0) d) (0, + 3)
2. If an ellipse has focuses at (0, + 5) and vertices at (0, + 13) then the equation of an ellipse will be

a) x 2 y 2 1 b) x 2 y 2 1 c) x 2 y 2 1 d) None of these
169 144 169 25 144 169
4
3. If an ellipse has eccentricity is equal to and vertices at (0, + 10) then the equation of an ellipse will be
5
a) x 2 y 2 1 b) x 2 y 2 1 c) x 2 y 2 1 d) None of these
100 36 36 100 36 64
4. The length of the major axis for an ellipse 4x + y = 100
2
2
a) 20 b) 40 c) 60 d) None of these

Answers: 1. b) ( + 5, 0) 2. c) x 2 y 2 1 3. b) x 2 y 2 1 4. a) 20
144 169 36 100

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