A line is at a constant distance c from the origin and meets the

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 Multiple Choice QuestionsMultiple Choice Questions

271.

The products of lengths of perpendiculars from any point of hyperbola x2 - y2 = 8 to its asymptotes, is

  • 2

  • 3

  • 4

  • 8


272.

The equation 16x2 + y2 + 8xy - 74x - 78y + 212 = 0 represents

  • a circle

  • a parabola

  • an ellipse

  • a hyperbola


273.

Equation of curve in polar coordinates is lr = 2sin2θ2 represents

  • a straight line

  • a parabola

  • a circle

  • an ellipse


274.

iF a is a complex number and b is a real number, then the equation a + a + b = 0 represents a

  • straight line

  • parabola

  • circle

  • hyperbola


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275.

The equation of the circle of radius 5 and touching the co-ordinate axes in third quadrant is

  • (x - 5)2+ (y + 5)2 = 25 

  • (x + 5)2 + (y + 5)2 = 25

  • (x + 4)2 + (y + 4)2 = 25

  • (x + 6)+ (y + 6)= 25


276.

The four distinct points (0, 0), (2, 0), (0, - 2)and (k, - 2) are concyclic, if k is equal to

  • 3

  • 1

  • - 2

  • 2


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277.

A line is at a constant distance c from the origin and meets the coordinate axes in A and B. The locus of the centre of the circle passing through O, A, B is

  • x2 + y2 = c2

  • x2 + y2 = 2c2

  • x2 + y2 = 3c2

  • x2 + y2 = 4c2


D.

x2 + y2 = 4c2

Let the equation of the circle be    x2 + y2 + 2gx + 2fy + c = 0It passes through origin so c = 0Then, equation of circle isx2 + y2 + 2gx + 2fy = 0It also passes through Ax1, 0    x12 + 0 + 2gx1 = 0                          g = -x12It also passes through B0, y1 0 + y12 + 2fy1 - 0 f = -y12 centre of the circle is x12, y12Mid point of AB is x12, y12i. e.                          OM = AM = BMThus        c = OM  c = x12 + y12                      x12 + y12  = 4c2Thus, locus is  x2 + y2  = 4c2


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278.

The line y = mx + c intercepts the circle x2 + y2 = r2 in two distinct points, if

  • - r1 + m2 < c < r1 + m2 

  •  c < - r1 + m2 

  •  c < r1 + m2 

  • None of the above


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279.

The equation of the parabola with the focus (3, 0) and the directrix x + 3 = 0, is

  • y2 = 3x

  • y2 = 6x

  • y2 = 12x

  • y2 = 2x


280.

If e and e' are the eccentricities of the ellipse 5x2 + 9y2 = 45 and the hyperbola 5 - 4y = 45 respectively, then ee' is equal to

  • 1

  • 4

  • 5

  • 9


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