Line x+ ay =1 cuts the circle `x^(2)+y^(2)-4x-2y+1=0` at two points A and B such that Chord AB subtends an angle of `90^(@)` at origin then sum of possible values of a is

Line x+ay=1 cuts the circle x^(2)+y^(2)-4x-2y+1=0 at two points A and B such that Chord AB subtends an angle of 90^(@) at origin then sum of possible values of alpha is

Line 3x + by = k intersect the curve 2x^2 + 3y^2 + 2xy=1 at points A and B. Thecircle on AB as diameter passes through origin,then sum of all possible values of 'k' is

If the line y=mx-(m-1) cuts the circle x^(2)+y^(2)=4 at two real and distinct points then

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 the line through the origin which cuts the circle x^(2)+y^(2)-4x-2y-20=0 at the points A an B such that AB=4sqrt(5), is

The line x cos alpha+y sin alpha=p, intersects the circle x^(2)+y^(2)=4 at A and B .If the chord AB makes an angle 30^(@) at a point on the circumference of the circle,then p^(2)=

A line y=2x+K cuts the curve (x-3)^(2)+(y-4)^(2)=25 at A and B and if bar(AB) subtends 90^(@) at origin then the value of K equals

If line y= 2x meets circle x^(2) + y^(2) - 4x = 0 in point A and B , then equation of circle of which AB is diameter is

If line y = 4x meets circle x^(2) + y^(2) - 17 x = 0 in points A and B , then equation of circle of which AB is a diameter is