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 circle x^2+y^2-4x-8y-5=0 intersects the line 3x-4y=m at two distinct points, then find the values of mdot

If the equation p x^2+(2-q)x y+3y^2-6q x+30 y+6q=0 represents a circle, then find the values of pa n dqdot

Find the value of a for which the lines 2x+y-1=0 2x+y-1=0 a x+3y-3=0 3x+2y-2=0 are concurrent.

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 planes x-c y-b z=0,c x-y+a z=0a n d b x+a y-z=0 pass through a straight line, then find the value of a^2+b^2+c^2+2a b c dot

Find the value of a for which the lines represented by a x^2+5x y+2y^2=0 are mutually perpendicular.

If the straight line x - 2y + 1 = 0 intersects the circle x^2 + y^2 = 25 at points P and Q, then find the coordinates of the point of intersection of the tangents drawn at P and Q to the circle x^2 + y^2 = 25 .

Find the image of the circle x^2+y^2-2x+4y-4=0 in the line 2x-3y+5=0

If the lines 2x + y - 3 = 0 , 5x + ky - 3 = 0 " and " 3x - y - 2 = 0 are concurrent , find the value of k.