If P is a point such that the ratio of the square of the lengths

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 Multiple Choice QuestionsMultiple Choice Questions

281.

The pole of the straight line x + 4y = 4 with respect to the ellipse x2 + 4y2 = 4 is

  • (1, 1)

  • (1, 4)

  • (4, 1)

  • (4, 4)


282.

Locus of the poles of focal chord of a parabola is

  • the axis

  • a focal chord

  • the directrix

  • the tangent at the vertex


283.

The equation 1r = 18 + 38cosθ represents

  • a parabola

  • an ellipse

  • a hyperbola

  • a rectangular hyperbola


284.

If the circle x2 + y2 + 6x - 2y + k = 0 bisects the circumference of the circle x2 + y2 + 2x - 6y - 15 = 0, then k is equal to:

  • 21

  • - 21

  • 23

  • - 23


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285.

If P is a point such that the ratio of the square of the lengths of the tangents from P to the circles x2 + y2 + 2x - 4y - 20 = 0 and x2 + y2 - 4x + 2y - 2y - 44 = 0 is 2 : 3, then the locus of P is a circle with centre :

  • (7, - 8)

  • (- 7, 8)

  • (7, 8)

  • (- 7, - 8)


B.

(- 7, 8)

Let co-ordinates of P be x1, y1.Given that,            x2 + y2 + 2x - 4y - 20 = 0     ...iand    x2 + y2 - 4x +  2y -44 = 0     ...iiLength of the tangent from P to Eq. i       =  x12 + y12 + 2x1 - 4y1 - 20    ...iiiLength of the tangent from P to Eq. ii       =  x12 + y12 - 4x1 +  2y1 -44    ...ivGiven that ratio of lengths of tangent = 23  x12 + y12 + 2x1 - 4y1 - 20  x12 + y12 - 4x1 +  2y1 -44  = 233x12 + 3y12 + 6x1 - 12y1 - 60 = 0      = 2x12 + 2y12 - 8x1 + 4y1 - 88 x12 + y12 + 14x1 - 16y1 + 28 = 0 Locus of points is x2 + y2 + 14x1 - 16y1 + 28 = 0Centre of the circle is - 7, 8.


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286.

If 5x - 12y + 10 = 0 and 12y - 5x + 16 = 0 are two tangents to a circle, then the radius of the circle is

  • 1

  • 2

  • 4

  • 6


287.

The eccentricity of the ellipse 9x2 + 5y2 - 18x - 20y - 16 = 0, is:

  • 12

  • 23

  • 32

  • 2


288.

The product of the lengths of perpendiculars drawn from any point on the hyperbola x2 - 2y2 - 2 = O to its asymptotes is

  • 12

  • 23

  • 32

  • 2


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289.

The equation of the parabola with focus (0, 0)and directrix x + y = 4 is

  • x2 + y2 - 2xy + 8x +8y -16 = 0

  • x2 + y2 - 2xy + 8x + 8y = 0

  • x2 + y2 + 8x + 8y - 16= 0

  • x2 - y2 + 8x +8y - 16= 0


290.

The number of circles that touch all the three lines x + y - 1 = 0, x - y - 1 = 0 and y + 1 = 0 is

  • 2

  • 3

  • 4

  • 1


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