Given the circle C with the equation x2 + y2 - 2x + 10y - 38

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 Multiple Choice QuestionsMultiple Choice Questions

361.

If  is the area of the triangle formed by the positive x-axis and the normal and tangent to the circle x+ y2 = 4 at (1, 3) then is equal to

  • 32

  • 3

  • 23

  • 6


 Multiple Choice QuestionsMatch The Following

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362.

Given the circle C with the equation x+ y2 - 2x + 10y - 38 = 0. Match the List I with the List II given below concerning C
  List I   List II
A The equation of the polar of (4, 3)with respect to C I y + 5 = 0
B The equation of the tangent at (9, - 5) on C II x = 1
C The equation of  the normal at(- 7, - 5) on C III 3x + 8y = 27
D The equation of the diameter of  C passing through (1,3) IV x + y = 3
    V x = 9

The correct answer is

A. A B C D (i) III I V II
B. A B C D (ii) IV V I II
C. A B C D (iii) III V I II
D. A B C D (iv) IV II I V


A.

A B C D

(i)

B.

A B C D

(ii)

C.

A B C D

(iii)

D.

A B C D

(iv)


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363.

For the circle C with the equation x2 + y2 - 16 - 12y + 64 = 0 match the List I with the List II given below.
  List I   List II
(i) The equation of the polar of (- 5, 1) with respect to  (A) y = 0
(ii) The equation of the tangent at (8, 0) to C (B) y = 6
(iii) The equation of the normal at (2, 6) to C (C) 13x + 5y = 98
(iv) The equation of the diameter of C through (8, 12) (D) 13x + 5y = 98
    (E) x = 6

The correct match is

A. (i) (ii) (iii) (iv) (i) (D) (B) (A) (E)
B. (i) (ii) (iii) (iv) (ii) (D) (A) (B) (E)
C. (i) (ii) (iii) (iv) (iii) (C) (D) (A) (B)
D. (i) (ii) (iii) (iv) (iv) (C) (E) (B) (A)

 Multiple Choice QuestionsMultiple Choice Questions

364.

The circle 4x2 + 4y2 - 12x - 12y + 9 = 0

  • Touches both the axes

  • Touches the x-axis only

  • Touches the y-axis only

  • Does not touch the axes


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365.

If the length of the tangent from (h, k) to the circle x2 + y2 = 16 is twice the length of the tangent from the same point to the circle x2 + y2 + 2x + 2y = 0, then

  • h2 + k2 + 4h + 4k + 16 = 0

  • h2 + k2 + 3h + 3k = 0

  • 3h2 + 3k2 + 8h + 8k + 16 = 0

  • 3h2 + 3k2 + 4h + 4k + 16 = 0


366.

(α, 0) and (b, 0) are centres of two circles belonging to a coaxial system of which y-axis is the radical axis. If radius of one of the circles is 'r', then the radius of the other circle is

  • r2 + b2 + a212

  • r2 + b2 - a212

  • r2 + b2 - a213

  • r2 + b2 + a213


367.

If the circle x2 + y+ 4x - 6y + c =0 bisects the circumference of the circle x2 + y2 - 6x + 4y - 12 = 0, then c is equal to

  • 16

  • 24

  • - 42

  • - 62


368.

A circle of radius 4, drawn on a chord of the parabola y2 = 8x as diameter, touches the axis of the parabola. Then, the slope of the chord is

  • 12

  • 34

  • 1

  • 2


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369.

The mid-point of a chord of the ellipse x2 + 4y2 - 2x + 20y = 0 is (2, - 4). The equation of the chord is

  • x - 6y = 26

  • x + 6y = 26

  • 6x - y = 26

  • 6x + y = 26


370.

If the focus of the ellipse x225 + y216 = 1 and the hyperbola x24 - y2b2 = 1 coincide, then b2 =?

  • 4

  • 5

  • 8

  • 9


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