If the circles `x^2+y^2+2a x+c y+a=0` and `x^2+y^2-3a x+d y-1=0` intersects at points P and Q , then find the values of `a` for which the line `5x+b y-a=0` passes through `Pa n dQdot`

Find the angle at which the circles x^2+y^2+x+y=0 and x^2+y^2+x-y=0 intersect.

If the circles x^(2)+y^(2) +5Kx+2y + K=0 and2(x^(2)+y^(2))+2Kx +3y-1=0, (KinR) , intersect at the points P and Q, then the line 4x + 5y - K = 0 passes through P and Q, for

If the circles x^(2)+y^(2) +5Kx+2y + K=0 and2(x^(2)+y^(2))+2Kx +3y-1=0, (KinR) , intersect at the points P and Q, then the line 4x + 5y - K = 0 passes through P and Q, for x^(2)+y^(2)-16x-20y+164=r^(2) and (x-4)^(2)+(y-7)^(2) = 36 intersect at two distinct points, then

If the circles x ^(2) + y ^(2) + 5x -6y-1=0 and x ^(2) + y^(2) +ax -y +1=0 intersect orthogonally (the tangents at the point of intersection of the circles are at right angles), the value of a is

If line x-2y-1=0 intersects parabola y^(2)=4x at P and Q, then find the point of intersection of normals at P and Q.

If line x-2y-1=0 intersects parabola y^(2)=4x at P and Q, then find the point of intersection of normals at P and Q.

If the lines 2x-3y+1=0 and 3x-2y+1=02x-3y+1=0 and 3x-2y+1=0 intersect the cordinate axsing through points centre of the circle passing through those points is

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