Origin is the centre of a circle passing through the vertices of an equilateral triangle whose median is of length 3a, then the equation of the circle is

The circle x²+y²=4x+8y+5=0 intersects the line 3x-4y=m at two distinct points if

The line 2x+3y+19-0and 9x+6y-17=0 cut the coordinate axes in

The midpoint of the chord formed by the polar of (-9, 12) w.r.t x²+y²=100 is

For the circle x²+y²-6x+8y-1=0, the points (2, 3) (-2, -1) are

The condition that the chord xcosα+ysinα-p=0 of x²+y²-a²=0 may subtend a right angle at he cnetre of the circle is

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