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

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

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

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

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

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

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