Mathematics - Circle

Question - 1

Length of the diameter of circle \({ X }^{ 2 }+{ Y }^{ 2 }-8X+6Y-5=0\) is

  • A \(4\sqrt{30}\)
  • B \(2\sqrt{30}\)
  • C \(3\sqrt{30}\)
  • D 30

Question - 2

Find the equation of circle having centre \(\left( \frac { 1 }{ 2 } ,\frac { 1 }{ 4 } \right) \) and radius \(\frac{1}{12}\)

  • A \(36{ x }^{ 2 }+36{ y }^{ 2 }-36x-18y-11=0\)
  • B \(36{ x }^{ 2 }+36{ y }^{ 2 }+36x+18y+11=0\)
  • C \(36{ x }^{ 2 }+36{ y }^{ 2 }-36x-18y+11=0\)
  • D None of the above

Question - 3

Equation of the diameter of the circle \({ x }^{ 2 }+{ y }^{ 2 }-12x+4y+6=0\) is given by

  • A x + y = 0
  • B x + 3y = 0
  • C x = y
  • D 3x + 2y = 0

Question - 4

Equation of the circle with centre on the Y-axis and passing through the origin and the point (2, 3) is

  • A \({ x }^{ 2 }+{ y }^{ 2 }+13y=0\)
  • B \({ 3x }^{ 2 }+{ 3y }^{ 2 }+13x+3=0\)
  • C \({ 6x }^{ 2 }+{ 6y }^{ 2 }-26y=0\)
  • D \({ x }^{ 2 }+{ y }^{ 2 }+13x+3=0\)

Question - 5

The equation of the circle which passes through the origin and makes intercept of lengths a and b on the X and Y-axes respectively, are

  • A \({ x }^{ 2 }+{ y }^{ 2 }\pm ax\pm by=0\)
  • B \({ x }^{ 2 }\pm { y }^{ 2 }=0\)
  • C \({ x }^{ 2 }\pm ax\pm by=0\)
  • D None of the above

Question - 6

Find the equation of the circle which passes through the points (2, 3) and (4, 5) and the centre lies on the straight line Y - 4X + 3 = 0.

  • A \({ x }^{ 2 }+{ y }^{ 2 }-4x-10y+25=0\)
  • B \({ x }^{ 2 }+{ y }^{ 2 }-4x-10y-25=0\)
  • C \({ x }^{ 2 }+{ y }^{ 2 }-4x+10y-25=0\)
  • D None of the above

Question - 7

Find the equation of a circle which touches both the axes and the line 3X - 4Y + 8 = 0 and lies in the third quadrant.

  • A \({ x }^{ 2 }+{ y }^{ 2 }+4x+4y-4=0\)
  • B \({ x }^{ 2 }+{ y }^{ 2 }-4x-4y+4=0\)
  • C \({ x }^{ 2 }+{ y }^{ 2 }+4x+4y+4=0\)
  • D None of the above

Question - 8

\({ X }^{ 2 }+{ Y }^{ 2 }+4X-6Y+4=0\) is the equation of the incircle of an equilateral triangle, then the equation of the circumcircle of the triangle is

  • A \({ x }^{ 2 }+{ y }^{ 2 }+4x+6y-23=0\)
  • B \({ x }^{ 2 }+{ y }^{ 2 }+4x-6y-23=0\)
  • C \({ x }^{ 2 }+{ y }^{ 2 }-4x-6y-23=0\)
  • D None of the above

Question - 9

The circle \({ X }^{ 2 }+{ Y }^{ 2 }-2X+4Y+3=0\) has a square inscribed in it. Sides of the square are parallel to the coordinate axes. Then, one vertex of the square is

  • A \(\left( 1+\sqrt { 2 } ,-2 \right) \)
  • B \(\left( 1-\sqrt { 2 } ,-2 \right) \)
  • C \(\left( 1,-2+\sqrt { 2 } \right) \)
  • D None of the above

Question - 10

The circle \({ x }^{ 2 }+{ y }^{ 2 }={ r }^{ 2 }\) intersects the line Y = mX + c at the two real distinct points, if

  • A \(-r\sqrt { 1+{ m }^{ 2 } }\)
  • B \(-c\sqrt { 1-{ m }^{ 2 } }\)
  • C \(-r\sqrt { 1-{ m }^{ 2 } }\)
  • D None of the above
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