The locus of the midpoints of the chords of the circle 4x²+4y²-12x+4y+1=0 which subtend an angle of π/3 at its centre is a circle of radius

Let P be a point on the circle x²+y²=9, Q a point on the line 7x+y+3=0, and  the perpendicular bisector of PQ be the line x-y+1=0. Then the coordinates of P are

If the of the circle passing through the points (3,4),(3,2),(1,4) is x²+y²+2ax+2by+c=0, then the ascending order of a, b, c is

(1, 2) is a point on the circle x²+y²+2x-6y+5=0 which is orthogonal to x²+y²=5. The  conjugate  point  of (1, 2) w. r. to the circle x²+y² =5 and which lies on the first circle is

Let C₁=x²+y²-2x-4y=0, C₂=x²+y²+2x+10y=0 and L=2x+7y+7=0 Then L is the

The equation of the circle having centre on the line x+y=1 and touching the lines 3x-4y+2=0, 4x+3y+7= 0 is

The equation of the circle passing through the points (4, 1), (6, 5) and having the centre on line 4x+y-16=0 is

From any point on the circle x²+y²+2gx+2fy+c=0 tangents are drawn to the circle x²+y²+2gx+2fy+c sin²α+(g²+f²) 13cos² α =0

The area of the triangle formed by the positive x-axis and the tangent and the normal at (1, √3) to the circle x²+y²=4 is

The locus of the points from which the lengths of the tangents to the two circles x² + y² + 4x + 3 = 0, x² + y²-6x +5 = 0 are in the ratio 2 : 3 is a circle with centre