If a chord of the circle `x^(2)+y^(2)-4x-2y-c=0` is trisected at the points `((1)/(3),(1)/(3))and((8)/(3),(8)/(3))` then

If a chord of the circle x^2+y^2-4x-2y-c=0 is trisected at the points (1/3,1/3)&(8/3,8/3) , then ' c ' equal to: 10 (b) 20 (c) 40 (d) none of these

The equation of the chord of the circle x^(2)+y^(2)-6x+8y=0 which is bisected at the point (5, -3), is

The equation of the chord of the circle x^(2)+y^(2)-4x+6y-3=0 having (1,-2) as it midpoint is

The line 3x -4y = k will cut the circle x^(2) + y^(2) -4x -8y -5 = 0 at distinct points if

The chord of contact of (3,-1) w.r.t the circle x^(2)+y^(2)+2x-4y+1=0 is

Find the equation of polar of the point (i) (3,-1) with resect to the cirlce 2x^(2)+2y^(2)=11 (ii) (2,3) with respect to the circle x^(2)+y^(2)+6x+8y-96=0 (iii) (4,3) with respect to the circle x^(2)+y^(2)-8x-6y-9=0 (iv) (1,2) with respect to the cirlce x^(2)+y^(2)=7 (v) (1,-2) with respect to the circle x^(2)+y^(2)-10x-10y+25=0

If the hyperbola xy=c^(2) intersects the circle x^(2)+y^(2)=a^(2)" is four points "P(x_(1),y_(1)), Q(x_(2),y_(2)), R(x_(3),y_(3)) and S(x_(4),y_(4)) then show that (i) x_(1)+x_(2)+x_(3)+x_(4)=0 (ii) y_(1)+y_(2)+y_(3)+y_(4)=0 (iii) x_(1)x_(2)x_(3)x_(4)=c^(4) (iv) y_(1)y_(2)y_(3)y_(4)=c^(4)

The chord of contact of the pair of tangents drawn from any point on 3x+4y=8 to the circle x^2 + y^2 = 4 passes through a fixed point. (A) (1/2, 15/8) (B) (2, 3/2) (C) (3/2, 2) (D) none of these

Find the equation of the chord of the circle x^2 + y^2 + 6x+8y+9=0 , whose middle point is (-2, -3) .

The two circles x^(2)+y^(2)-2x-3=0 and x^(2)+y^(2)-4x-6y-8=0 are such that