The equation of the circle which passes through the points of int

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 Multiple Choice QuestionsMultiple Choice Questions

121.

The equation of the tangent to the conic x2 - y2 - 8x + 2y + 11 = 0 at (2, 1) is

  • x + 2 = 0

  • 2x + 1 = 0

  • x + y + 1 = 0

  • x - 2 = 0


122.

The total number of tangents through the point ( 3, 5) that can be drawn to the ellipses 3x2 + 5y2 = 32 and 25x + 9y2 = 450 is

  • 0

  • 2

  • 3

  • 4


123.

The equation of chord of the circle x2 + y2 - 4x = 0, whose mid-point is (1, 0) is

  • y = 2

  • y = 1

  • x = 2

  • x = 1


124.

The line y = 2t2 intersects the ellipse x29 + y24 = 1 in real points, if

  • t  1

  • t < 1

  • t > 1

  • t  1


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125.

The coordinates of the focus of the parabola described parametrically by x = 5t2 + 2, y = 10t + 4 are

  • (7, 4)

  • (3, 4)

  • (3, - 4)

  • (- 7, 4)


126.

The angle between the lines joining the foci of an ellipse to one particular extremity of the minor axis is 90°. The eccentricity of the ellipse is

  • 1/8

  • 1/√3

  • √(2/3)

  • √(1/2)


127.

If the rate of increase of the radius of a circle is 5 cm/ s, then the rate of increase of its area, when the radius is 20 cm, will be

  • 10π

  • 20π

  • 200π

  • 400π


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128.

The equation of the circle which passes through the points of intersection of the circles x2 + y2 - 6x = 0 and x2 + y2 - 6y = 0 and has its centre at 32, 32, is

  • x2 + y2 + 3x + 3y + 9 = 0

  • x2 + y2 + 3x + 3y = 0

  • x2 + y2 - 3x - 3y = 0

  • x2 + y2 - 3x - 3y + 9 = 0


C.

x2 + y2 - 3x - 3y = 0

The equations of given circles are,

x2 + y2 - 6x = 0         ...(i)

x2 + y2 - 6y = 0        ...(ii)

On solving Eqs. (i) and (ii), we get

x = 0, y = 0 or x = 3, y = 3

 Points of intersection are (0, 0) and (3 3).Also, centre of required circle is 32, 32 g = - 32 and f = - 32Hence, equation of circle is,x2 + y2 - 3x - 3y + c = 0

Since, this circle passes through (0, 0), thus equation of circle becomes

x2 + y2 - 3x - 3y + c = 0


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129.

If 2y = x and 3y + 4x = 0 are the equations of a pair of conjugate diameters of an ellipse, then the eccentricity of the ellipse is

  • 23

  • 25

  • 13

  • 12


130.

If t is a parameter, then x = at + 1t, y = bt - 1t represents

  • an ellipse

  • a circle

  • a pair of straight lines

  • a hyperbola


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