The limiting points of the co-axial system containing the two cir

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 Multiple Choice QuestionsMultiple Choice Questions

261.

If the line x + 2by + 7 = 0 is a diameter of the circle x2 + y2 - 6x + zy = 0, then b is equal to

  • - 5

  • - 3

  • 2

  • 5


262.

If the line y = 2x+ c is tangent to the parabola y2 = 4x, then c is equal to

  • - 12

  • 12

  • 13

  • 14


263.

The length of the latus rectum of the ellipse 9x2 + 4y2 = 1 is

  • 32

  • 49

  • 83

  • 89


264.

The number of circles that touch all the straight lines x + y = 4,x - y = - 2 and y = 2 is

  • 1

  • 2

  • 3

  • 4


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265.

The equation of the normal to the circle x2 + y2 + 6x + 4y - 3 = 0 at (1, - 2) is

  • y + 1 = 0

  • y + 2 = 0

  • y + 3 = 0

  • y - 2 = 0


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266.

The limiting points of the co-axial system containing the two circles x2 + y2 + 2x - 2y + 2 = 0 and 25(x2 + y) - 10x - 80y + 65 = 0 are

  • (1, - 1), (- 3, - 40)

  • 1, - 1, - 15, 85

  • - 1, 1, 15, 85

  • - 15, - 85


C.

- 1, 1, 15, 85

Equation of circles are                x2 + y2 + 2x - 2y + 2 = 0           ...iand x2 + y2 - 25x - 165y + 135 = 0           ...ii x2 + y2 + 2x - 2y + 2    + λx2 + y2 - 25x - 165y + 135 = 0 1 + λx2 + 1 + λy2 + 21 - λ5x          - 21 + 8λ5y + 2 + 13λ5 = 0 x2 + y2 + 21 - λ51 + λx        - 21 + 8λ51 + λy + 2 + 13λ51 + λ = 0          ....(iii)At  = 0  1 - λ51 + λ = 0  λ = 5Then, x2 + y2 - 3y + 52 = 0 Centre is 0, 32The limiting points are - 1, 1, 15, 85.


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267.

The radical axis of circles x2 + y2 + 5x + 4y - 5 = 0 and x2 + y2 - 3x + 5y - 6 = 0 is

  • 8y - x + 1 = 0

  • 8x - y+ 1 = 0

  • 8x - 8y + 1 = 0

  • y - 8x + 1 = 0


268.

The length of latusrectum of parabola y2 + 8x - 2y + 17 = 0 is

  • 2

  • 4

  • 8

  • 16


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269.

If the normal to the parabola y2 = 4x at P(1, 2) meets the parabola again in Q, then coordinates of Q are

  • (- 6, 9)

  • (9, - 6)

  • (- 9, - 6)

  • (- 6, - 9)


270.

The eccentricity of ellipse x216 + y29 = 1 is

  • 716

  • 54

  • 74

  • 72


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