The equation of the circle which passes through the origin and cu

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331.
The equation of the circle which passes through the origin and cuts orthagonally each of the circles x2 + y2 - 6x + 8 = 0 and x2 + y2 - 2x - 2y = 7 is
  • 3x2 + 3y2 - 8x - 13y = 0

  • 3x2 + 3y2 - 8x + 29y = 0

  • 3x2 + 3y2 + 8x + 29y = 0

  • 3x2 + 3y2 - 8x - 29y = 0


B.

3x2 + 3y2 - 8x + 29y = 0

Let the required equation of circle be  x2 + y2 + 2gx + 2fy = 0. Since, the above circle cuts the given circles orthagonally.

   2- 3g + 2f0 = 8                      2g = - 83and       - 2g - 2f = - 7 2f = + 7 + 83 = 293 Required equation of circle isx2 + y2 - 83x + 293y = 0

or 3x2 + 3y2 - 8x + 29y = 0


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332.

The number of normals drawn to the parabola y2 = 4x from the point (1, 0) is

  • 0

  • 1

  • 2

  • 3


333.

If the distance between foci of an ellipse is 6 and the length of the minor axis is 8, then the eccentricity is

  • 15

  • 12

  • 35

  • 45


334.

If the circle x2 + y2 = a2 intersects the hyperbola xy = c2 in four points (xi, yi), for i = 1, 2, 3 and 4, then y1 + y2 + y3 + y4 equals

  • 0

  • c

  • a

  • c4


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335.

The mid point of the chord 4x - 3y = 5 of the hyperbola 2x2 - 3y2 = 12 is

  • 0, - 53

  • (2, 1)

  • 54, 0

  • 114, 2


336.

The eccentricity of conic5r = 2 +3cosθ + 4sinθ is

  • 12

  • 1

  • 32

  • 52


337.

The radius of the sphere x2 + y2 + z2 = 12x + 4y +3z is

  • 132

  • 13

  • 26

  • 52


338.

The equation of the radical axis of the pair of circles  7x2 + 7y2 - 7x + 14y + 18 = 0  and 4x2 + 4y2 - 7x + 8y + 20 = 0 is

  • x - 2y - 5 = 0

  • 2x - y + 5 = 0

  • 21x - 68 = 0

  • 23x - 68 = 0


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339.

x2 + y2 - 8x + 40 = 05x2 + 5y2 -25x + 80 = 0x2 + y2 - 8x + 16y + 160 = 0From the point P are equal, then P = ?

  • 8, 152

  • - 8, 152

  • 8, - 152

  • - 8, - 152


340.

The equation of the circle concentric with the circle x2 + y2 - 6x + 12y + 15 = 0 and of double its area is

  • x2 + y2 - 6x +12y - 15 = 0

  • x2 + y2 - 6x +12y - 30 = 0

  • x2 + y2 - 6x +12y - 25 = 0

  • x2 + y2 - 6x +12y - 20 = 0


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