JEE Questions for Maths Circle And System Of Circles Quiz 2 - MCQExams.com

If x/α + y/β = 1 touches the circles x2 + y2 = a2, then point (1/α, 1/β) lies on a/ am
  • straight line
  • circle
  • parabola
  • ellipse
Angle between tangents drawn to circles x2 + y2 = 20, from the point (6,is
  • π/2
  • π
  • π/4
  • 2π
The locus of a point which moves, so that the ratio of the length of the tangents to the circle x2 + y2 + 4x + 3 = 0 and x2 + y2 - 6x + 5 = 0 is 2 : 3 is
  • 5x2 + 5y2 - 60x + 7 = 0
  • 5x2 + 5y2 - 60x - 7 = 0
  • 5x2 + 5y2 - 60x - 7 = 0
  • 5x2 + 5y2 + 60x + 7 = 0
Two tangents to the circle x2 + y2 = 4 at the points A and B meet at P(-4, 0). The area of the quadrilateral PAOB, where O is the origin, is
  • 4 sq units
  • 6√2 sq units
  • 4√3 sq units
  • None of these
If y = 3x is the tangent to a circle with centre (1, 1), then the other tangent drawn through (0,to the circle is
  • 3y = x
  • y = - 3x
  • y = 2x
  • y = - 2x
The equations of the tangents to circle 5x2 + 5y2 = 1, parallel to line 3x + 4y = 1 are
  • 3x + 4y = ±2√5
  • 6x + 8y = ±√5
  • 3x + 4y = ±√5
  • None of these
The measure of the chord intercepted circle x2 + y2 = 9 and the line x - y + 2 = 0 is
  • √28
  • 2√5
  • 7
  • 5
The location for the l1x + m1y + n1 = 0 to be conjugate with respect to the circle x2 + y2 = r2, is
  • r2 (ll1 + mm= nm1
  • r2 (ll1 - mm= nm1
  • r2 (ll1 + mm+ nm1 = 0
  • r2 (ll1 + mm= nn1
The locus of the mid - points of the chord of the circle x2 + y2 = 4 which subtends a right angle at the origin is
  • x + y = 2
  • x2 + y2 = 1
  • x2 + y2 = 2
  • x+ y = 1
The locus of the point of intersection of the tangents at the extremeties of a chord of the circle x2 + y2 - 2ax = 0 passes throught the point, is
  • (a/2, 0)
  • (0, a/2)
  • (a, 0)
  • (0, 0)
If the lines joining the origin to the intersection of the line y = mx + 2 and the circle x2 + y2 = 1 are at right angles, then
  • m = √3
  • m = ±√7
  • m = 1
  • m = √5
The equation of the chord of the circle x2 + y2 = 81, which is bisected at the point (-2, 3), is
  • 3x - y = 13
  • 3x - 4y = 13
  • 2x - 3y = 13
  • 3x - 3y = 13
  • 2x - 3y = -13
If the circle x2 + y2 - 2x - 2y - 7 = 0 and x2 + y2 + 4x + 2y + k = 0 cut orthogonally, then the length of the common chord of the circle is
  • 12/√13
  • 2
  • 5
  • 8
If the circles x2 + y2 + 4x + 22y + c = 0 bisects the circumference of the circle x2 + y2 - 2x + 8y - d = 0, then (c + d) is equal to
  • 30
  • 50
  • 40
  • 56
  • 52
Which of the following is a point on the common chord of the circle x2 + y2 + 2x - 3y + 6 = 0 and x2 + y2 + x - 8y - 13 = 0 ?
  • (1, - 2)
  • (1, 4)
  • (1, 2)
  • (1, - 4)
A variable chord is drawn through the orihgin to the circle x2 + y2 - 2ax = 0. The locus of the centre of the circle drawn on this chord as diameter, is
  • x2 + y2 + ax = 0
  • x2 + y2 - ax = 0
  • x2 + y2 + ay = 0
  • x2 + y2 - ay = 0
The centre of the circle, whose radius is 5 and which touches the circle x2 + y2 - 2x - 4y - 20 = 0 at (5,is
  • (10, 5)
  • (5, 8)
  • (5, 10)
  • (8, 9)
  • (9, 8)
A circle passes through the points (0,and (0,and also touches the circle x2 = 16. The radius of the circle is
  • 1
  • 2
  • 3
  • 4
  • 5
If the squares of the length of tangents from a point P to the circles x2 + y2 = a2, x2 + y2 = b2 and x2 + y2 = c2 are in AP, then
  • a, b, c are in AP
  • a, b, c are In GP
  • a2, b2, c2 are in AP
  • a2, b2, c2 are in GP
The point at which the circles x2 + y2 - 4x - 4y + 7 = 0 and x2 + y2 + y2 - 12x - 10y + 45 = 0 touch each other, is

  • Maths-Circle and System of Circles-12500.png
  • 2)
    Maths-Circle and System of Circles-12501.png

  • Maths-Circle and System of Circles-12502.png

  • Maths-Circle and System of Circles-12503.png
The locus of the centre of the circle, which cuts the circle x2 + y2 - 20x + 4 = 0 orthogonally and touches the line x = 2, is
  • x2 = 16y
  • y2 = 4x
  • y2 = 16x
  • x2 = 4y
The circles x2 + y2 - 6x - 8y = 0 and x2 + y2 - 6x + 8 = 0 are
  • intersecting in two points
  • non - interescting
  • touching externally
  • touching internally
The total number of common tangents of x2 + y2 - 6x - 8y + 9 = 0 and x2 + y2 = 1 is
  • 4
  • 2
  • 3
  • 1
If the two circles (x + 7)2 + (y - 3)2 = 36 and (x - 5)2 + (y + 2)2 = 49 touch each other externally, then the point of contact is

  • Maths-Circle and System of Circles-12504.png
  • 2)
    Maths-Circle and System of Circles-12505.png

  • Maths-Circle and System of Circles-12506.png

  • Maths-Circle and System of Circles-12507.png

  • Maths-Circle and System of Circles-12508.png
The centres of three circles x2 + y2 = 1, x2 + y2 + 6x - 2y = 1 and x2 + y2 - 12x + 4y = 1 are
  • collinear
  • non-collinear
  • nothing to be said
  • None of these
The equation of the circle which passes through the origin and cuts orthogonally each of the circles x2 + y2 - 6x + 8 = 0 and x2 + y2 - 2x - 2y - 7 = 0 is
  • 3x2 + 3y2 - 8x - 13y = 0
  • 3x2 + 3y2 - 8x + 29y = 0
  • 3x2 + 3y2 + 8x + 29y = 0
  • 3x2 + 3y2 - 8x - 29y = 0
If the circles x2 + y2 + 4x + 8y = 0 and x2 + y2 + 8x + 2ky = 0 touch each other, then K is equal to
  • 12
  • 8
  • - 8
  • 4
The equation of the circle passing through the point (1,and through the points of intersection of the circles x2 + y2 = 6 and x2 + y2 - 6y + 8 = 0 is
  • x2 + y2 + 3y - 13 = 0
  • x2 + y2 - 3y + 1 = 0
  • x2 + y2 + 3x + 1 = 0
  • 5x2 + 5y2 + 6y + 16 = 0
For the given circles x2 + y2 - 6x - 2y + 1 = 0 and x2 + y2 + 2x - 8y + 13 = 0, which of the following is correct ?
  • One circle lies inside the other
  • One circle lies completely outside the other
  • Two circles intersect in two points
  • They touch each other externally
If a circle passes through the point (1,and cuts the circle x2 + y2 = 4 orthogonally, then the equation of the locus of its centre is
  • x2 + y2 - 3x - 8y + 1 = 0
  • x2 + y2 - 2x - 6y - 7 = 0
  • 2x + 4y - 9 = 0
  • 2x + 4y - 1 = 0
The limiting points of coaxial system determined by the circles x2 + y2 + 5x + y + 4 = 0 and x2 + y2 + 10x - 4y - 1 = 0 are
  • (0,and (2, 1)
  • (0, -and (-2, - 1)
  • (0,and (1, 2)
  • (0, -and (2, 1)
Two circles x2 + y2 - 2x - 3 = 0 and x2 + y2 - 4x - 6y - 8 = 0 are such that
  • they touch internally
  • they touch externally
  • they intersect at two points
  • they are non-intersecting
If the circles x2 + y2 = 9 and x2 + y2 + 2ax + 2y + 1 = 0 touch each other internally, then α is equal to
  • ± 4/3
  • 1
  • 4/3
  • - (4/3)
The circles x2 + y2 - 4x - 6y - 12 = 0 and x2 + y2 + 4x + 6y + 4 = 0
  • touch externally
  • do not intersect
  • intersect at two points
  • are concentric
  • None of these
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 (3/2, 3/2), is . `
  • x2 + y2 + 3x + 3y + 9 = 0
  • x2 + y2 + 3x + 3y = 0
  • x2 + y2 - 3x - 3y = 0
  • x2 + y2 - 3x + 3y + 9 = 0
The circles x2 + y2 + 6x + 6y = 0 and x2 + y2 - 12x - 12y = 0
  • cut orthogonally
  • touch each other internally
  • intersect two points
  • touch each other externally
If the length of the tangent from any point on the circle (x - 3)2 + (y + 2)2 = 5r2 to the circle (x - 3)2 + (y + 2)2 = r2 is 16 units, then the area between the two circles (in sq units) is
  • 32π
  • 4π
  • 8π
  • 256π
The circles ax2 + ay2 + 2g1x + 2f1y + c1 = 0 and bx2 + by2 + 2g2x + 2f2y + c2 = 0 (a ≠ 0 and b ≠cut orthogonally, if
  • g1g2 +f1f2 = ac1 + bc2
  • 2(g1g2 + f1f= bc1 + ac2
  • bg1g2 + af1f2 = bc1 + ac2
  • g1g2 + f1f2 = c1 + c2
The number of common tangents to the two circles x2 + y2 - 8x + 2y = 0 and x2 + y2 - 2x - 16y + 25 = 0 is
  • 1
  • 2
  • 3
  • 4
The number of common tangents to the circles x2 + y2 = 4 and x2 + y2 - 6x - 8y + 24 = 0, is
  • 3
  • 4
  • 2
  • 1
If (-3,lies on the circle x2 + y2 + 2gx + 2fy + c = 0 which is concentric with the circle x2 + y2 + 6x + 8y - 5 = 0, then c is equal to
  • 11
  • - 11
  • 24
  • 100
The condition for the coaxial system x2 + y2 + 2λx + c = 0, where λ is a parameter and c is a constant to have distinct limiting points, is
  • c = 0
  • c < 0
  • c = -1
  • c > 0
If the radical axis of the circles x2 + y2 + 2gx + 2fy + c = 0 and 2x2 + 2y2 + 3x + 8y + 2c = 0, touches the circle x2 + y2 + 2x + 2y + 1 = 0, then
  • g = 3/4 anf f ≠ 2
  • g ≠ 3/4 anf f = 2
  • g = 3/4 and f = 2
  • None of these
The two circles x2 + y2 - 5 = 0 and x2 + y2 - 2x - 4y - 15 = 0
  • touch each other externally
  • touch each other internally
  • cut each other orthogonally
  • do not intersect
The two circles x2 + y2 - 2x + 6y + 6 = 0 and x2 + y2 - 5x + 6y + 15 = 0 touch each other
  • externally
  • internally
  • coincide
  • None of these
The circles x2 + y2 - 10x + 16 = 0 and x2 + y2 = r intersect each other at two distinct points, if
  • r < 2
  • r4 > 8
  • 2 < r < 8
  • 2 ≤ r ≤ 8
The radical axis of the coaxial system of circles with limiting points (1,and (- 2,is
  • x+ 3y = 0
  • 3x + y = 0
  • 2x + 3y = 0
  • 3x + 2y = 0
The number of common tangents to circles x2 + y2 + 2x + 8y - 23 = 0 and x2 + y2 - 4x - 10y + 9 = 0, is/are
  • 1
  • 3
  • 2
  • None of these
If the circles x2 + y2 + 2gx + 2fy = 0 and x2 + y2 + 2g\'x + 2f \' y = 0 touch each other, than
  • ff ' = gg'
  • fg = f ' g'
  • (fg)2 = (f ' g ')2
  • fg' = f ' g
If two circles of the same radius r and centres at (2.and (5,respectively cut orthogonally, then the value of r is
  • 3
  • 2
  • 1
  • 5
0:0:1


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