Show that for all values of `lambda `, the lines joining the origin to the points common to `x^2+2hxy-y^2+gx+fy=0 ` and fx -gy= `lambda` are at right angles .

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

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

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

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 .

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.

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 pair of lines joining origin to the points of intersection of, the two curves ax^2+2hxy + by^2+2gx = 0 and a^'x^2 +2h^'xy + b^'y^2 + 2g^'x = 0 will be at right angles, if

Find the angle between the lines joining the point (0,0),(2,3) and the points (2,-2),(3,5)dot

.......... of the following is the line joining the point of intersection y-x + 7=0 and y+ 2x - 2=0 and origin.

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.