The polar of the point(t-1, 2t) w.r.t the circle x²+y²-4x-6y+4=0 passes through the point of intersection of the lines

A rectangle ABCD is inscribed in a circle with a diameter lying along the line 3y=x+10. If A=(-6, 7), B=(4, 7) then the area of the rectangle is

The equation to the circle touching the y-axis at the origin and passing through(b, c) is

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