The equation of the ellipse having vertices at (± 5, 0) an

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 Multiple Choice QuestionsMultiple Choice Questions

131.

The equation (x - x1)(x - x2) + (y - y1)(y - y2) = 0 represents a circle whose centre is

  • x1 - x22, y1 - y22

  • x1 + x22, y1 + y22

  • (x1, y1)

  • (x2, y2)


132.

The circles x2 + y2 + 6x + 6y = 0 and x2 + y2 - 12x - 12y = 0

  • cut orthogonally

  • touch each other internally

  • intersect in two points

  • touch each other externally


133.

The two parabolas x2 = 4y and y2 = 4x meet in two distinct points. One of these is the origin and the other is

  • (2, 2)

  • (4, - 4)

  • (4, 4)

  • (- 2, 2)


134.

The vertex of the parabola x2 + 2y = 8x - 7 is

  • 92, 0

  • 4, 92

  • 2, 92

  • 4, 72


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135.

If P(at2, 2at) be one end of a focal chord of the parabola y2 = 4ax, then the length of the chord is

  • at - 1t2

  • at - 1t

  • at + 1t

  • at + 1t2


136.

The length of the common chord of the parabolas y2 = x and x2 = y is

  • 22

  • 1

  • 2

  • 12


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137.

The equation of the ellipse having vertices at (± 5, 0) and foci (± 4, 0) is

  • x225 + y216 = 1

  • 9x2 + 25y2 = 225

  • x29 + y225 = 1

  • 4x2 + 5y2 = 20


B.

9x2 + 25y2 = 225

The vertices and foci of an ellipse are (± 5, 0) and (± 4, 0) respectively.

 a = 5 and ae = 4

 e = 45

We know that,        e = 1 - b2a2 1625 = 1 - b225  b2 = 9Hence, equation of an ellipse is,x225 + y29 = 1  9x2 + 25y2 = 225


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138.

The area included between the parabolas y2 = 4x and x2 = 4y is

  • 83 sq unit

  • 8 sq unit

  • 163 sq unit

  • 12 sq unit


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139.

The locus of the centres of the circles which touch both the axes is given by

  • x2 - y2 = 0

  • x2 + y2 = 0

  • x2 - y2 = 1

  • x2 + y2 = 1


140.

The latusrectum of an ellipse is equal to one-half of its minor axis. The eccentricity of the ellipse is

  • 16

  • 32

  • 34

  • 12


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