The equations of the tangents to the circle x²+y²+8x-4y-5=0 and perpendicular to 2x+3y+5=0 are

For the circle2x²+2y²-5x-4y-3=0, the point (4, 2)

If the lines 2x+y+12=0, kx-3y-10=0 are conjugate w.r.t the circle x²+y²-4x+3y-1=0, then k=

Equation of the circle touching the y-axis at (0, √3) and cuts the x-axis in the points (- 1, 0) and (-3, 0) is

The equation of the common tangent at the point contact of the circles x²+y²-10x+2y+10=0, x²+y²-4x-6y+12=0 is

The number of tangents that can be drawn from (6, 0) to the circle x²+y²-4x-6y-12=0 are

The locus of the middle points of portions of the tangents to the circle x²+y²=a² terminated by the axes is

If the length of the tangets from two points A, B to a circles are 6, 7 respectively. If A, B are conjugate points then AB=

The length of the tangent from a point on the circle x²+y²+2gx+2fy+c=0 to the circle x²+y²+2gx+2fy+c^’=0 is

The normal of the circle(x-2)²+(y-1)²=16 which bisects the chord cut off by the line x-2y-3=0 is