Show that the equation of the circle passing through (1, 1) and the points of intersection of the circles `x^2+y^2+13 x-3 y=0` and `2x^2+2y^2+4x-7y-25=0` is `4x^2+4y^2+30 x-13 y-25=0.`

Find the equation of the circle passing throught (1,1) and the points of intersection of the circles x^(2)+y^(2)+13x-3y=0 and 2x^(2)+2y^(2)+4x-7y-25=0

The equation of the line passing through the points of intersection of the circles 3x^2 +3y^2-2x + 12y-9=0 and x^2+y^2+6x+2y-15=0 is

Find the point of intersection of the circle x^2+y^2-3x-4y+2=0 with the x-axis.

Find the equations of the circles passing through the point (-4,3) and touching the lines x+y=2 and x-y=2

The equation of the circle passing through the point of intersection of the circles x^2+y^2-4x-2y=8 and x^2+y^2-2x-4y=8 and the point (-1,4) is (a) x^2+y^2+4x+4y-8=0 (b) x^2+y^2-3x+4y+8=0 (c) x^2+y^2+x+y=0 (d) x^2+y^2-3x-3y-8=0

Find the equation of the lines passing through the point of intersection lines 4x-y+3=0 and 5x+2y+7=0 Parallel to x-y+5=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 equation of the line passing through the points of intersection of 4x-y-3=0 and x+y-2=0 and perpendicular to 2x-5y+3=0.

find the equation of the circle with centre (2,3) and passing through the intersection of the lines 3x -2y -1=0 and 4x + y -27 =0 ..