If OA and OB are two equal chords of the circle `x^(2)+y^(2)-2x+4y=0` perpendicular to each other and passing through the origin,the slopes of OA and OB are the roots of the equations

If OA and OB are two perpendicular chords of the circle r=a cos theta+b sin theta epassing through origin,then the locus of the mid point of AB is :

If OA and OB be the tangents to the circle x^(2)+y^(2)-6x-8y+21=0 drawn from the origin O, then AB

The feet of the perpendicular from the origin on a variable chord of the circle x^(2)+y^(2)-2x-2y=0 is N If the variable chord makes an angle of 90^(@) at the origin, then the locus of Nhas the equation

The equation of chord of the circle x^(2)+y^(2)-6x4y12=0 which passes through the origin such thatorigin divides it in the ratio 3:2 is

The equation of the chord of the circle x^(2)+y^(2)-3x-4y-4=0, which passes through the origin such that the origin divides it in the ratio 4:1, is

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

A chord of the circle x^(2)+y^(2)-4x-6y=0 passing through the origin subtends an angle arctan(7/4) at the point where the circle meets positive y-axis.Equation of the chord is

If OA and OB are the tangents from the origin to the circle x^(2)+y^(2)+2gx+2fy+c=0 and C is the centre of the circle,the area of the quadrilateral OACB is