Find the equations of the straight lines joining the origin to the points of intersection of `x^2+y^2-4x-2y=0` and `x^2+y^2-2x-4y=4` .

The lines joining the origin to the points of intersection of 2x^2 + 3xy -4x +1 = 0 and 3x + y=.1 given by

The lines joining the origin to the point of intersection of x^2+y^2+2gx+c=0 and x^2+y^2+2fy-c=0 are at right angles if

Find the equation of the straight line passing through the point (2,1) and through the point of intersection of the lines x+2y = 3 and 2x-3y=4

Prove that The lines joining the origin to the points of intersection of the line 3x-2y =1 and the curve 3x^2 + 5xy -3y^2+2x +3y= 0 , are are at right angles.

Prove that the straight lines joining the origin to the point of intersection of the straight line h x+k y=2h k and the curve (x-k)^2+(y-h)^2=c^2 are perpendicular to each other if h^2+k^2=c^2dot

Find the equation to the pair of straight lines joining the origin to the intersections oi the straight line y=mx + c and the curve x^2 + y^2=a^2 . Prove that they are at right angles if 2c^2=a^2(1+m^2) .

The equation of the line joining the point {3, 5) to the point of intersection of the lines 4x + y - 1 = 0 and 7x - 3y - 35 = 0 is equidistant from the points (0,0) and (8,34) .

If the straight lines joining origin to the points of intersection of the line x+y=1 with the curve x^2+y^2 +x-2y -m =0 are perpendicular to each other , then the value of m should be

Prove that the angle between the lines joining the origin to the points of intersection of the straight line y=3x+2 with the curve x^2+2x y+3y^2+4x+8y-11=0 is tan^(-1)((2sqrt(2))/3)

If the straight line joining the origin and the points of intersection of y=mx+1 and x^2+y^2=1 be perpendicular to each other , then find the value of m.