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

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

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

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

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

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: 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

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

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

If 1,ω,ω² are the cube roots of unity, then (1-ω+ ω²)5+(1+ω- ω²)⁵ is equal to