If the lines joining the origin and the point of intersection of curves `a x^2+2h x y+b y^2+2gx+0` and `a_1x^2+2h_1x y+b_1y^2+2g_1x=0` are mutually perpendicular, then prove that `g(a_1+b_1)=g_1(a+b)dot`

If the lines joining the origin and the point of intersection of curves ax^(2)+2hxy+by^(2)+2gx+0 and a_(1)x^(2)+2h_(1)xy+b_(1)y^(2)+2g_(1)x=0 are mutually perpendicular,then prove that g(a_(1)+b_(1))=g_(1)(a+b)

Find the equation of the lines joining the origin to the points of intersection of x^2 + y^2 =1 and x + y = 1.

Find the value if k , if the lines joining the origin with the points of intersection of the curve 2x^(2)-2xy+3y^(2)+2x-y-1=0 and the x + 2y = k are mutually perpendicular .

Show that the lines joining the origin to the two points of intersection of the curves ax^(2)+2hxy+by^(2)+2gx=0, a_(1)x^(2)+2h_(1)xy+b_(1)y^(2)+2g_(1)x=0 will be at right angles to one another if g(a_(1)+b_(1))=g_(1)(a+b)

Show that lines joining the origin to the points of intersection of 2(x^(2)+y^(2))=1 and x+y=1 coincide.

Find the angle between the lines joining the origin to the points of intersection of the curve x^2+2xy+y^2+2x+2y-5=0 and the line 3x-y+1=0.

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.