The line y=x+a√2 touches the circle x²+y²=a² at P. The coordinates of P are

Equation of the tangent to the circle x²+y²=3, which is include at 60⁰ with the x-axis is

The centre of the incircle of the triangle formed by the line 3x+4y=24 with the axes is

The equation of the circle which cuts orthogonally the  three circles x²+y²+2x+17y+4=0, x²+y²+7x+6y+11=0 , x²+y²-x+22y+3=0 is

If a chord of the circle x²+y²=8 makes equal intercepts of length a on the coordinate axes, then |a|<

I:The equation whose roots are the squares of the roots of x³-x²+8x-6=0 is x³+15x²+52x+36=0

II:The equation whose roots are the cubes of the roots x³+3x²+2=0 is x³+33x²+12x+8=0

If the circles x²+y²+2ax+4ay-3a²=0 and x²+y²-8ax-6ay+7a²=0 touch each other externally, the point of contact is

The equation of the circle whose centre lies in the first quadrant and which touches the coordinate axes and the line (x/3)+(y/4)=1 is x²+y²-2cx-2cy+c²=0, then c=

The equation to the locus of the midpoints of chords of the circle x2+y2-8x+6y+20=0 which are parallel to 3x + 4y+5 = 0 is

The radical centre of the circle x²+y²=1, x²+y²-2x=1, x²+y²-2y=1 is