If y=4x-5 is a tangent to the curve y²=px³+q at (2, 3), then

For the circles x²+y²+4x+2y-4=0, x²+y²-4x-2y+4=0 the line 3x+4y-5=0 is a

The locus of midpoints of the chord of the circle x²+y² = 25 which pass through a fixed point (4, 6) is a circle. The radius of that circle is

If one end of the diameter of the circle x²+y²-6x+4y-12=0 is (7, -5),  then the other end of the diameter is

Polar of the origin w.r.t the circle x²+y²+2ax+2by+c=0 touches the circle x²+y²=r² if

The circle orthogonal to the  three circles x²+y²+a_ix+b_iy+c=0, i=1, 2, 3 is

The coaxal system having limiting points (2,3), (-3, 2) is

If the two circles (x-1)²+(y-3)²=r² and x²+y²-8x+2y+8=0 intersect in two distinct points, then

The pole of a straight line with respect to the circle x²+y²=a² lies on the circle x²+y²=9a². If the straight line touches the circle x²+y²=r², then

P(-2, -1) and (0, -3) are the limiting points of a coaxal system of which C= x²+y²+5x+y+4=0 is a member. The circle S= x²+y²-4x-2y-15=0 is orthogonal to the circle C. The point where the polar P cuts the circle S is