JEE Maths - Circle

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Question - 1

If a chord of the circle x2 + y2 = 8 makes equal intercepts of length a on the coordinate axes and the range of values of | a | is (0, k), then find | k |, where [ ] represents the greatest integer function.

  • A 2
  • B 1
  • C 3
  • D 4

Question - 2

A regular hexagon is formed by two equilateral triangles inscribed in the circle x2 + y2 = 4. If S isthe area of the hexagon (in sq. units), then find the greatest integer contained in S.

  • A 5
  • B 4
  • C 6
  • D 3

Question - 3

The angle between a pair of tangents drawn from a point P to the circle x2+ y2 + 4x -6y + 9sin2\(\alpha\) + l3cos2 \(\alpha\) = 0 is 2\(\alpha\). The equation of locus of point P is x2 + y2 ax + by + c = 0. Evaluate b2 - ac.

  • A 4
  • B 5
  • C 2
  • D 0

Question - 4

The point P ( 10, 7) lies outside the circle x2 + y2 - 4x + 2y - 20 = 0. Find the greatest distance of point P from the circle.

  • A 12
  • B 13
  • C 14
  • D 15

Question - 5

Let O be the origin, OP and OQ be two perpendicular chords of equal length of the circle x2 +y2- 4x + 8 = 0. Let m1 and m2 be the slopes of chords OP and OQ. Evaluate \(|\frac{m_1}{m_2}|\), where m1 > m2

  • A 3
  • B 5
  • C 2
  • D 9

Question - 6

If one of the diameters of the circle given by the equation x2 + y2 + 4x - 6y - 12 = 0 is a chord of a circle S whose centre is at (3, -2), find radius of circle S. (Take \(\sqrt3\) = 1.73)

  • A 8.95
  • B 8.78
  • C 8.75
  • D 8.65

Question - 7

A square is inscribed in the circle x2+ y2' - 2x + 4y - 93 = 0 with it's sides parallel to the coordinate axes. If (xi, yi), i = 1,2,3, 4 denote the vertices, then find \(\left|\sum x_{i}\right|+\left|\sum y_{i}\right|\)

  • A 10
  • B 08
  • C 11
  • D 12

Question - 8

The equation of incircle of \(\Delta\)OAB, where AB is the intercept of the line 5x + l2y = 60 between the coordinate axes and O is the origin, is x2 + y2 + ax + by + c = 0. Evaluate abc.

  • A 66
  • B 67
  • C 65
  • D 64

Question - 9

If OA and OB be the tangents to the circle x2+ y2- 8x - 6y + 16 = 0 drawn from the origin O, then find |AB| .

  • A 4.2
  • B 4.9
  • C 4.7
  • D 4.8

Question - 10

OM and ON are represented by y = (2+\(\sqrt3\))x, and y = (2 -\(\sqrt3\))x, O being the origin. If  \(\angle \mathrm{OMP}=90^{\circ}=\angle \mathrm{ONP}\) and p = (3, 4), then find the radius of \(\Delta\)PMN

  • A 4
  • B 3.5
  • C 3
  • D 2.5
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