Let a circle be given by `2x(x-a)+y(2y-b)=0,(a!=0,b!=0)` . Find the condition on `a and b` if two chords each bisected by the x-axis, can be drawn to the circle from `(a , b/2)`

A given line L_1 cut x and y-axes at P and Q respectively and has intercepts a and b/2 on x and y-axes respectively. Let another line L_2 perpendicular to L_1 cut x and y-axes at R and S respectively. Let T be the point of intersection of PS and QR . If two chords each bisected by x-axis can be drawn from (a, b/2) to the locus of T , then (A) a^2 gt 2b^2 (B) b^2 gt 2a^2 (C) a^2 lt 2b^2 (D) b^2 lt 2a^2

Find the length of the chord intercepted by the circle x^(2)+y^(2)-8x-6y=0 on the line x-7y-8=0 .

Find the length of the chord of contact with respect to the point on the director circle of circle x^2+y^2+2a x-2b y+a^2-b^2=0 .

Find the length of the chord of contact with respect to the point on the director circle of circle x^2+y^2+2a x-2b y+a^2-b^2=0 .

Find the number of common tangents that can be drawn to the circles x^2+y^2-4x-6y-3=0 and x^2+y^2+2x+2y+1=0

Find the length of the chord intercepted by the circle x^(2) + y^(2) = 25 on the line 2x -y + 5= 0

Find the equation to the chord of contact of the tangents drawn from an external point (-3, 2) to the circle x^2 + y^2 + 2x-3=0 .

Find the equation to the chord of contact of the tangents drawn from an external point (-3, 2) to the circle x^2 + y^2 + 2x-3=0 .

Find the locus of the feet of the perpendiculars drawn from the point (b, 0) on tangents to the circle x^(2) + y^(2) =a^(2)

Find the locus of the midpoint of the chords of the circle x^2+y^2-ax-by=0 which subtend a right angle at the point (a/2 ,b/2)dot is