Page 84 - Mathematics Class - XI

Case-Study Based Questions
Case-Study Based Questions

Let the two foci of an ellipse be (–1, 0) and (3, 4) and the foot of the perpendicular form the focus (3, 4)
upon a tangent to the ellipse be (4, 6).

Now, read the above paragraph carefully and answer the following questions.
1. The foot of the perpendicular from the focus (–1, 0) upon the same tangent to the ellipse is

(a) 12 34 (b) 7 11 (c) 2, 17 (d) 12,

,
,

5 5 3 3 4
2. The equation of the auxiliary circle of the ellipse is
(a) x + y –2x – 4y – 5 = 0 (b) x + y – 2x – 4y – 20 = 0
2
2
2
2
(c) x + y + 2x + 4y – 20 = 0 (d) x + y + 2x + 4y – 5 = 0
2
2
2
2
3. The length of the semi-minor axis of the ellipse is
(a) 1 (b) 22 (c) 17 (d) 19
4. The equation of the directrix of the ellipse are
21 17
(a) x – y + 2 = 0, x – y – 5 = 0 (b) x + y – = 0, x + y + = 0
2 2
3 5 31 19
(c) x – y + = 0, x – y – = 0 (d) x + y – = 0, x + y + = 0
2 2 2 2
5. The point of contract to the tangent with the ellipse is
(a) 40 68 (b) 4 8 (c) 8 17 (d) 41 83

,

,
,

,

11 11 7 7 5 5 13 13
Assertion-Reason Based Questions
Assertion-Reason Based Questions
Directions for Questions 1 to 2: In each of the questions given below, there are two statements marked as
Assertion (A) and Reason (R). Mark your answer as per the codes provided below:
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false. (d) A is false but R is true.
Q. 1. Assertion (A) : In an ellipse, the sum of the distances between foci is always less than the sum of
focal distance of any point on it.
Reason (R) : The eccentricity of an ellipse is less than 1.
Q. 2. Assertion (A) : x – y – 5 = 0 is the equation of the tangent to the ellipse 9x + 16y = 144.
2
2
Reason (R) : The equation of the tangent to the ellipse x 2 2 y 2 2 1 is of the form
y = mk + am + b 2 a b
2
2

Answers

Case-Study Based Questions: 1. (a) 2. (a) 3. (c) 4. (d) 5. (a)

Assertion-Reason Based Questions: 1. (a) 2. (a) 3. (c)

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