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
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
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
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
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
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)
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)
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
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
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
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
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
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
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
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
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
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
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)
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)
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)
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
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
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
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
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)
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
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
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
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)
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