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

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

i. Find the point of intersection of the lines 2x +y-3=0, 3x-y-2=0  ii. Find the equation of the line passing through the above point of intersection and parallel to the line x + y + 1 = 0.

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

If a circle passes through the point of intersection of the lines lambdax- y +1=0 and x-2y+3=0 with the coordinate axis, then value of lambda is

The point of intersection of the circle x^(2) + y^(2) = 8x and the parabola y^(2) = 4x which lies in the first quadrant is

Find the equation of straight line joining the points of intersection of the lines 3x+2y+1=0 and x+y=3 to the intersection of the lines y-x=1 and 2x+y+2=0