If line `2x-by + 1 = 0` intersects the curve `2x^2-by^2 + (2b-1)xy-x -by = 0` at points `A & B and AB` subtends a right angle at origin, then value of `b+b^2` is equal to

If the portion of the line ax - by - 1 = 0 , intercepted between the lines ax + y + 1 = 0 and x + by = 0 subtends a right angle at the origin , then find value of 4a +b^2 + (b+1)^2 .

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 a is

The line 3x+6y=k intersects the curve 2x^(2)+3y^(2)=1 at points A and B .The circle on AB as diameter passes through the origin. Then the value of k^(2) 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 x+2y=k intersects the curve x^(2)-xy+y^(2)+3x+3y-2=0 at two points A and B and if 0 is the origin. Then the condition for angleAOB=90^(@) is

The line 3x+6y=k intersects the curve 2x^2+3y^2=1 at points A and B . The circle on A B as diameter passes through the origin. Then the value of k^2 is__________

The line 3x+6y=k intersects the curve 2x^2+3y^2=1 at points A and B . The circle on A B as diameter passes through the origin. Then the value of k^2 is__________

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

A line passing through (1,0) intersects the curve 2x^(2)+5y^(2)-7x=0 in A and B then the angle substended by the line AB at the origin is