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

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

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

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

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

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

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

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

Match the following

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