The eccentricity of the ellipse, which meets the straight line&nb

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 Multiple Choice QuestionsMultiple Choice Questions

171.

Equation of the chord of the hyperbola 25x2  - 16y2 = 400 which is bisected at the point (6, 2), is

  • 6x - 7y = 418

  • 75x - 16y = 418

  • 25x - 4y = 400

  • None of these


172.

The centres of a set of circles, each of radius 3, lie on the circles x2 + y2 = 25. the locus of any point in the set is

  • 4  x2 +_y2  64

  • x2 + y2  25

  • x2 + y2  25

  • 3  x2 + y2  9


173.

The angle of intersection of the circles x2 + y2 - x + y - 8 = 0 and x2 + y2 + 2x + 2y - 11 = 0 is

  • tan-1199

  • tan-119

  • tan-1919

  • tan-19


174.

If a tangent having slope of - 43 to the ellipse x218 + y232 = 1 intersects the major and minor axes in points A and B respectively, then the area of OAB is equal to (O is centre of the ellipse)

  • 12 sq units

  • 48 sq units

  • 64 sq units

  • 24 sq units


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175.

The locus of mid-points of tangents intercepted between the axes of ellipse x2a2 + y2b2 = 1 will be

  • a2x2 + b2y2 = 1

  • a2x2 + b2y2 = 2

  • a2x2 + b2y2 = 3

  • a2x2 + b2y2 = 4


176.

If PQ is a double ordinate of hyperbola (x2/a2) - (y2/b2) = 1 such that OPQ is a equilateral triangle, O being the centre of the hyperbola, then the eccentricity 'e' of the hyperbola satisfies

  • 1 < e < 2/√3

  • e = 2/√3

  • e = √3/2

  • e > 2/√3


177.

The lines 2x - 3y - 5 = 0 and 3x - 4y = 7 are diameters of a circle of area 154 sq units, then the equation of the circle is

  • x2 + y2 + 2x - 2y - 62 = 0

  • x2 + y2 + 2x - 2y - 47 = 0

  • x2 + y2 - 2x + 2y - 47 = 0

  • x2 + y2 - 2x + 2y - 62 = 0


178.

The angle of depressions of the top and the foot of a chimney as seen from the top of a second chimney, which is 150 m high and standing on the same level as the first are θ and ∅ respectively, then the distance between their tops when tan θ = 4/3 and tan ∅ = 5/2 is

  • 150/√3 m

  • 100√3 m

  • 150 m

  • 100 m


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179.

If (-3, 2) lies on the circle x2 + y2 + 2gx + 2fy + c = 0, which is concentric with the circle x2 + y2 + 6x + By - 5 = 0, then c is equal to

  • 11

  • - 11

  • 24

  • 100


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180.

The eccentricity of the ellipse, which meets the straight line x7 + y2 = 1 on the axis of x and the staraight line x3 - y5 = 1 on the axis of y and whose axes lie along the axes of coordinate, is

  • 327

  • 267

  • 37

  • None of the above


B.

267

Let the equation of the ellipse be x2a2 + y2b2 = 1. It is given that it passes through (7, 0) and (0, - 5). Therefore, a2 = 49 and b= 25

The eccentricity of the ellipse is,

e = 1 - b2a2   = 1 - 2549 = 2449   = 267


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