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`

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

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

Find the point of intersection of the straight lines : x/3-y/4=0, x/2+y/3 =1 .

The equation of the line joining the origin to the point of intersection of the lines 2x^2+xy-y^2+5x-y+2=0 is

Find the point of intersection of the straight lines : 2x + 3y-6 = 0, 3x - 2y-6= 0 .

Find the equation to the pair of straight lines joining the origin to the intersections of 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) .

Find the area enclosed by the straight line y=x+2 and the curve x^(2)=y

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

If the lines joining the origin to the intersection of the line y=nx+2 and the curve x^2+y^2=1 are at right angles, then the value of n^2 is

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