px + qy =40 is a chord of minimum length of circle `(x-10)^(2)+(y-20)^(2)=729`.If the chord passes through (5,15) then `p^(2013)+q^(2013)` is equal to

The minimum length of the chord of the circle x^(2)+y^(2)+2x+2y-7=0 which is passing (1,0) is :

PQ is a chord of the circle x^(2)+y^(2)-2x-8=0 whose mid-point is (2, 2). The circle passing through P, Q and (1, 2) is

If ax+by-5=0 is the equation of the chord of the circle (x-3)^(2)+(y-4)^(2)=4 which passes through (2, 3) and at the greatest distance from the centre of the circle then |a+b| is equal to

The least length of chord passing through (2,1) of the circle x^(2)+y^(2)-2x-4y-13=0 is

For the circle x^(2)+y^(2)-2x-6y+1=0 the chord of minimum length and passing through (1,2) is of length-

the length of the chord of the circle x^(2)+y^(2)=25 passing through (5, 0) and perpendicular to the line x+y=0 , is

If y=2x is a chord of the circle x^(2)+y^(2)-10x=0, find the equation of a circle with this chord as diameter.

The length of the shortest chord of the circles x^(2)+y^(2)+2gx+2fy+c=0 which passes through the point (a,b) inside the circle is