Eamcet - Maths - Circles

If (1, a), (b, 2) are conjugate points with respect to the circle x2 + y2 = 25, then4a + 2b is equal to :

A.  25

B.  50

C.  100

D.  150

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The angle between the tangents drawn from (0,0) to the circle x2+y2+4x-6y+4=0 is

A.  Sin-1 5/13

B.  Sin-1 5/12

C.  Sin-1 12/13

D.   π/2

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If the circle x2 + y2 + 2x + 3y + 1 = 0 cuts another circle x2+y2 + 4x + 3y + 2 = 0 in A and B, then the equation of the circle with AB as a diameter is :

A.  x2 + y2 + x  + 3y + 3 = 0

B.  2x2 +2y2 + 2x + 6y + 1 = 0

C.  x2 + y2 +x +6y + 1 = 0

D.  2x2 + 2y2 + x + 3y +1 = 0

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The extremities of a diameter of a circle have coordinates (-4, -3) and (2, -1). The length of the segment cut off by the circle on y-axis is

A.  5√13

B.  14

C.  3√13

D.  √55

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The number of common tangents to the two circles x2+y2-x=0, x2+y2+x=0 is

A.  2

B.  1

C.  4

D.  3

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The centres of similitude of the circles x2+y2-2x-6y+9=0, x2+y2=1 is

A.  (1/3, 1), (-1, -3)

B.  (1/5, -1), (-1, -5)

C.  (1/3, 1), (1, 3)

D.  (-1/3, -1), (-1, -3)

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The inverse point of (1, 2) with respect to the circle x2+y2-4x-6y+9=0 is

A.  (0, 0)

B.  (1, 0)

C.  (0, 1)

D.  (1, 1)

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If the polars of points on the circle x2+y2= a2 w.r.t the circle x2+y2= b2  touch the circle x2+y2= c2, then a, b, c are in

A.  A.P

B.  G.P

C.  H.P

D.  A.G.P

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If the equation of the circle which cuts orthogonally the circle x2+y2-4x+2y-7=0 and having centre at (2, 3) is x2+y2+2ax+2by+c=0 then the ascending order of a, b, c is

A.  a, b, c

B.  b, c, a

C.  b, a, c

D.  a, c, b

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The parametric equation of the circle x2+y2+x+√3y=0 is

A.  x=cosθ, y=sinθ

B.  x+(1/2)=cosθ, y+(√3/2)=sinθ

C.  x-(1/2)=cosθ, y-(√3/2)

D.  none of these

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How many circles can be drawn each touching all the three lines x+y=1, x+1=y, 7x-y=6

A.  1

B.  2

C.  3

D.  4

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Equation of the circle passing through A(1, 2), B(5, 2) so that the angle substended by AB at points on the circle is π/4 is

A.  x2+y2-6x-8=0

B.  x2+y2-6x-8y+17=0

C.  x2+y2-6x+8=0

D.   x2+y2-6x-8y-25=0

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Match the following Circle Radius I. x2+y2+4x-6y-12=0 a) 3 II. x2+y2-4x-2y-4=0 b) 5 III. x2+y2+6x+8y-96=0 c) 11

A.  a, b, c

B.  b, c, a

C.  b, a, c

D.  a, c, b

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The number of points where the circle x2+y2-4x-4y=1 cuts the sides of the rectangle x=2 , x=5 , y=-1 and y=5 is

A.  5

B.  1

C.  2

D.  3

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If 5x-12y+10=0 and 12y-5x+16=0 are two tangents to a circle,then the radius of the circle is

A.  1

B.  2

C.  4

D.  6

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The tangents at (3, 4), (4, -3) to the circle x2+y2=25 are

A.  coincide

B.  parallel

C.  perpendicular

D.  at an angle of 450

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The equation of the circle cutting orthogonally circles x2+y2+2x+8=0, x2+y2-8x+8=0 and which touches the line x-y+4=0 is

A.  x2+y2+4y=0

B.  x2+y2+8y+8=0

C.  x2+y2-16y-8=0

D.  x2+y2+16y-16=0

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If the circle S=x2+y2-16=0 intersects another circle S’=0 of radius 5 in such a manner that the common chord is of maximum length and has a slope equal to 3/4 then the centre of S’=0 is

A.  (9/5, -12/5) or (-9/5, 12/5)

B.  (9/5, 12/5) or (-9/5, -12/5)

C.  (9/7, -12/7) or (-9/7, 12/7)

D.  (9/7, 12/7) or (-9/7, -12/7)

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The locus of the midpoints of chords of the circle x2+y2=25 which touch the circle (x-2)2+(y-5)2=289 is

A.  (x2+y2-12x-5y)2=289(x2+y2)

B.  (x2+y2+12x+5y)2=87(x2+y2)

C.  (3x2-3y2-13x-3y)2=18(x2+y2)

D.  (x2+y2+15x+15y)2=89(x2-y2)

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If (3,2 )is limiting point of the coaxal system of circles whose common radical axis is 4x+2y=11, then the other limiting point is

A.  (1, 1)

B.  (2, 2)

C.  (2, 1)

D.  (3, 2)

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An equilateral triangle is inscribed in the circle x2+y2=a2 . The length of the side of the triangle is

A.  a√2

B.  a√3

C.  2a

D.  none

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The length of the intercept made by the circle x2+y2-12x+14y+11=0 on x-axis is

A.  9

B.  10

C.  8

D.  6

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I: The equation of the circle concentric with x2+y2-2x+8y-23=0 and passing through (2, 3) is x2+y2-2x+8y-33=0 II: : The equation of the circle passing through  the points (1, 1), (2, -1), (3, 2) is x2+y2-5x-y+4=0

A.  only I is true

B.  only II is true

C.  both I and II are true

D.  neither I nor lI true

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If  a circle passes through the point (a, b) and cuts the circle x2+y2=4 orthogonally, then the locus of its centre is

A.  2ax+2by+(a2+b2+4)=0

B.  2ax-2by-(a2+b2+4)=0

C.  2ax-2by+(a2+b2+4)=0

D.  2ax+2by-(a2+b2+4)=0

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The line 4x+4y-11=0 intersects the circle x2+y2-6x-4y+4=0 at A and B. The point of intersection of the tangents A, B is

A.  (-1, -2)

B.  (1, 2)

C.  (-1, 2)

D.  (1, -2)

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If 4l2-5m2+6l+1=0, then the line lx+my+1=0 touches the circle

A.  x2+y2+6x-4=0

B.  x2+y2+6x+4=0

C.  x2+y2+5x+4=0

D.  x2+y2-2x+5=0

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The equation of the circle whose radius is 5 and which touches the circle x2+y2-2x-4y-20=0 at the point (5, 5) is

A.  x2+y2-18x-16y+120=0

B.  x2+y2+18x+16y-120=0

C.  x2+y2-18x-16y-120=0

D.  x2+y2+18x+16y+120=0

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A: The polar of (2, 3) with respect to the circle x2+y2-4x-6y+5=0 is 2x+3y=0 R: The polar of (x1, y1) with respect to the circle S=0 is S1=0

A.  Both A and R are true and R is the correct explanation of A

B.  Both A and R are true but R is not correct explanation of A

C.  A is true but R is false

D.  A is false but R is true

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The locus of poles of tangets to the circle (x-p)2+y2=b2 w.r.t the circle x2+y2= a2 is

A.  (a2-px)2=b2(x2+y2)

B.  (a2-bx)2=p2(x2+y2)

C.  (a2+px)2=b2(x2+y2)

D.  (a2+bx)2=p2(x2+y2)

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The equation of the circle, with centre (3, -1) and which cuts off a chord of length 6 on the line 2x-5y+18=0 is

A.  x2+y2-6x+2y-28=0

B.  x2+y2+4x-6y+8=0

C.  x2+y2+4x-16y+18=0

D.  3x2+3y2+4x-6y+18=0

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