A ray of light emanating from `(-4, 3)` after reflection from x-axis at `(alpha-0)` is normal to circle `x^2 +y^2 -10x-2y+25=0`, then `4alpha=`

If the line |y|=x-alpha, such that alpha>0 does not meet the circle x^(2)+y^(2)-10x+21=0 , then alpha belongs to

Equation of normal at P(3,-4) to the circle x^(2)+y^(2)-10x-2y+6=0 is

If the line 3x-2y+p = 0 is normal to the circle x^(2)+ y^(2) = 2x-4y ,then p will be

If tangents are drawn from origin to the circle x^(2)+y^(2)-2x-4y+4=0, then

The normal at (1,1) to the circle x^(2)+y^(2)-4x+6y-4=0 is

The length of tangent from (0,0) to the circle x^(2)+y^(2)-14x+12y+25=0

A light ray gets reflected by y-axis. If the point of incidence is (0,-2) and reflected ray touches the circle x^(2) + y^(2) - 2x -2y +1=0 , then the equationof incident ray is

A light beam 2x+y+1=0 emanating from the point (-1,1) gets reflected from the straight line x+y+1=0 then reflected ray passes through