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

Find the angle at which the parabolas y^2=4x and x^2=32 y intersect.

Find the coordinates of the point at which the circles x^2-y^2-4x-2y+4=0 and x^2+y^2-12 x-8y+36=0 touch each other. Also, find equations of common tangents touching the circles the distinct points.

If the angle of intersection of the circle x^2+y^2+x+y=0 and x^2+y^2+x-y=0 is theta , then the equation of the line passing through (1, 2) and making an angle theta with the y-axis is (a) x=1 (b) y=2 (c) x+y=3 (d) x-y=3

Find the locus of the centres of the circle which cut the circles x^2+y^2+4x-6y+9=0 and x^2+y^2-5x+4y-2=0 orthogonally

Find the angle which the common chord of x^2+y^2-4y=0 and x^2+y^2=16 subtends at the origin.

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

Find the equations to the common tangents of the circles x^2+y^2-2x-6y+9=0 and x^2+y^2+6x-2y+1=0

Find the length of the common chord of the circles x^2+y^2+2x+6y=0 and x^2+y^2-4x-2y-6=0

Find the locus of a point which moves so that the ratio of the lengths of the tangents to the circles x^2+y^2+4x+3=0 and x^2+y^2-6x+5=0 is 2: 3.

Find the angle of intersection of the curves x y=a^2a n dx^2+y^2=2a^2