For the two circles x2 + y2 = 16 and x2 + y2 - 2y = 0 there

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 Multiple Choice QuestionsMultiple Choice Questions

111.

The locus of the passes through (a, 0), (- a, 0) is the centre of a circle which two variable points

  • x = 1

  • x + y = a

  • x + y = 2a

  • x = 0


112.

The intercept on the line y = x by the circle x2 = y2 - 2x = 0 is AB. Equation of the circle with AB as the diameter is

  • x2 + y2 = 1

  • x(x - 1) + y(y - 1) = 0

  • x2 + y2 = 2

  • (x - 1)(x - 2) + (y - 1)(y - 2) = 0


113.

If the coordinates of one end of a diameter of the circle x2 + y+ 4x-8y + 5 = 0 are (2, 1), the coordinates of the other end are

  • (- 6, - 7)

  • (6 , 7)

  • (- 6, 7)

  • (7, - 6)


114.

The locus of the middle points of all chords of the parabola y2 = 4ax passing through the vertex is

  • a straight line

  • an ellipse

  • a parabola

  • a circle


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 Multiple Choice QuestionsShort Answer Type

115.

Prove that the centre of the smallest circle passing through origin and whose centre lies on y = x + 1 is - 12, 12


 Multiple Choice QuestionsMultiple Choice Questions

116.

If t1 and t2 be the parameters of the end points of a focal chord for the parabola y2 = 4ax, then which one is true?

  • t1t2 = 1

  • t1t2 = 1

  • t1t2 = - 1

  • t1 + t2 = - 1


117.

S and T are the foci of an ellipse and B is end point of the minor axis. If STB is an equilateral triangle, the eccentricity of the ellipse is

  • 14

  • 13

  • 12

  • 23


118.

For different values of a, the locus of the point of intersection of the two straight lines 3x - y - 43α = 0 and 3αx + αy - 43 = 0

  • a hyperbola with eccentricity 2

  • an ellipse with eccentricity 23

  • a hyperbola with eccentricity 1916

  • an ellipse with eccentricity 34


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119.

The circles x2 + y2 - 10x + 16 = 0 and x2 + y2 = a2 intersect at two distinct points, if

  • a < 2

  • 2 < a < 8

  • a > 8

  • a = 2


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120.

For the two circles x2 + y2 = 16 and x2 + y2 - 2y = 0 there is/are

  • one pair of common tangents

  • only one common tangent

  • three common tangents

  • no common tangent


D.

no common tangent

Let, x2 + y2 = 16 and x2 + y2 - 2y = 0

The centres and radii of given circles are,

C10, 0, r1 = 4 and C20, 1, r2 = 0 + 1 = 1Now, C1C2 = 0 + 0 - 12 = 1

and r1 - r2 = 4 - 1 = 3

 C1C2 < r1 - r2

Hence, second circle lies inside the first circle.

Thus, no common tangents for these two circles.


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