The line ax + by + c = 0 intersects the line `x cosalpha + y sinalpha=c` at the point P and angle between them is `pi/4` . If the line `x sinalpha - y cosalpha = 0` also passes through the point P, then:

The angle between the lines x cos alpha + y sinalpha=a and xsinbeta- ycosbeta = a is

If a line passes through the point of intersection of the lines 2x+y=5,x-y=1 and having slope 2 then it also passes through the point

The distance between the points (a cosalpha, a sinalpha) and (a cosbeta, a sinbeta) where a> 0

The distance between the points (a cosalpha, a sinalpha) and (a cosbeta, a sinbeta) where a> 0

The distance between the points (a cosalpha, a sinalpha) and (a cosbeta, a sinbeta) where a> 0

The distance between the points (a cosalpha, a sinalpha) and (a cosbeta, a sinbeta) where a> 0

The distance between the points (a cosalpha, a sinalpha) and (a cosbeta, a sinbeta) where a> 0

The locus of the point of intersection of the lines x cosalpha + y sin alpha= p and x sinalpha-y cos alpha= q , alpha is a variable will be

Let C be the centroid of the triangle with vertices (3, -1) (1, 3) and ( 2, 4). Let P be the point of intersection of the lines x+3y-1=0 and 3x-y+1=0 . Then the line passing through the points C and P also passes through the point :