2x-y=4,x-2y+1=0

Thye angle between the lines x-2y+sqrt(15)=0& the circle x^(2)+y^(2)-4x-2y+1=0, 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

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

A variable circle which always touches the line x+2y-3=0 at (1, 1) cuts the circle x^2+y^2+4x-2y+1=0 . then all common chords of cricles pass through a fixed point(P,Q). THEN P+Q=

Find the equation of a circle which passes through the point (3, 2) and concentric with the circle x^(2)+y^(2)-4x +2y - 1=0 .

Find the equation of a circle which passes through the point (3, 2) and concentric with the circle x^(2)+y^(2)-4x +2y - 1=0 .

The line x+2y+a=0 intersects the circle x^2+y^2-4=0 at two distinct points A and B. Another line 12x-6y-41=0 intersects the circle x^2+y^2-4x-2y+1=0 at two distincts points C and D. The value of 'a' so that the line x+2y+a=0 intersects the circle x^2+y^2-4=0 at two distinct points A and B is

Find the number of possible common tangents of following pairs of circles (i) x^(2)+y^(2)-14x+6y+33=0 x^(2)+y^(2)+30x-2y+1=0 (ii) x^(2)+y^(2)+6x+6y+14=0 x^(2)+y^(2)-2x-4y-4=0 (iii) x^(2)+y^(2)-4x-2y+1=0 x^(2)+y^(2)-6x-4y+4=0 (iv) x^(2)+y^(2)-4x+2y-4=0 x^(2)+y^(2)+2x-6y+6=0 (v) x^(2)+y^(2)+4x-6y-3=0 x^(2)+y^(2)+4x-2y+4=0

Find the number of possible common tangents of following pairs of circles (i) x^(2)+y^(2)-14x+6y+33=0 x^(2)+y^(2)+30x-2y+1=0 (ii) x^(2)+y^(2)+6x+6y+14=0 x^(2)+y^(2)-2x-4y-4=0 (iii) x^(2)+y^(2)-4x-2y+1=0 x^(2)+y^(2)-6x-4y+4=0 (iv) x^(2)+y^(2)-4x+2y-4=0 x^(2)+y^(2)+2x-6y+6=0 (v) x^(2)+y^(2)+4x-6y-3=0 x^(2)+y^(2)+4x-2y+4=0

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