The equation of the circles whose radius is 3 and which touches the circle x²+y²+2x+6y-15=0 externally at the point (2, 1) is

cos(α+β+γ)+cos(α-β-γ)+cos(β-γ-α)+cos(γ-α-β) is equal to:

The equation of the circle passing through the point (1, 2) cutting the circle x²+y²-2x+8y+7=0 orthogonally and bisects the circumference of the circle x²+y²=9 is

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