The eccentricity of the hyperbola 4x2 - 9y2 = 36 is from Mathema

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 Multiple Choice QuestionsMultiple Choice Questions

101.

The transverse axis of a hyperbola is along the x - axis and its length is 2a. The vertex of the hyperbola bisects the line segment joining the centre and the focus. The equation of the hyperbola is

  • 6x2 - y2 = 3a2

  • x2 - 3y2 = 3a2

  • x2 - 6y2 = 3a2

  • 3x2 - y= 3a2


102.

A point moves in such a way that the difference of its distance from two points (8, 0) and (- 8, 0) always remains 4. Then, the locus of the point is

  • a circle

  • a parabola

  • an ellipse

  • a hyperbola


103.

Let C1 and C2 denote the centres of the circles x2 + y= 4 and (x - 2)2 + y2 = 1 respectively and let P and Q be their points of intersection. Then, the areas of C2PQ and CPQ are in the ratio

  • 3 : 1

  • 5 : 1

  • 7 : 1

  • 9 : 1


104.

The incentre of an equilateral triangle is (1, 1) and the equation of one side is 3x + 4y + 3 = 0. Then, the equation of the circumcircle of the triangle is

  • x2 + y2 - 2x - 2y - 2 = 0

  • x2 + y2 - 2x - 2y - 14 = 0

  • x2 + y2 - 2x - 2y + 2 = 0

  • x2 + y2 - 2x - 2y + 14 = 0


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105.

The eccentricity of the hyperbola 4x2 - 9y2 = 36 is

  • 113

  • 153

  • 133

  • 143


C.

133

Given equation can be rewritten as

x29 - y24 = 1Here, a = 3, b = 2 Eccentricity, e = a2 + b2a2                           = 9 + 49                           = 139                           = 133


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106.

The length of the latus rectum of the ellipse 16x2 + 25y2 = 400 is

  • 5/16 unit

  • 32/5 unit

  • 16/5 unit

  • 5/32 unit


107.

The vertex of the parabola y+ 6x - 2y + 13 = 0 is

  • (1, - 1)

  • (- 2, 1)

  • 32, 1

  • - 72, 1


108.

The coordinates of a moving point P are (2t2 + 4, 4t + 6). Then, its locus will be

  • circle

  • straight line

  • parabola

  • ellipse


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109.

The equation 8x2 + 12y2 - 4x + 4y - 1 = 0 represents

  • an ellipse

  • a hyperbola

  • a parabola

  • a circle


110.

If the straight line y = mx lies outside the circle x2 + y2 - 20y + 90 = 0, then the value of m will satisfy

  • m < 3

  • m < 3

  • m > 3

  • m > 3


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