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

If the lines joining the origin to the points of intersection of the line y=mx+2 and the curve x^(2)+y^(2)=1 are at right-angles, then

The lines joining the origin to the point of intersection of The lines joining the origin to the point of intersection of 3x^2+m x y=4x+1=0 and 2x+y-1=0 are at right angles. Then which of the following is not a possible value of m ? -4 (b) 4 (c) 7 (d) 3

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 condition that the pair of tangents drawn from origin to circle x^(2)+y^(2)+2gx+2fy+c=0 may be at right angles is

The angle between the lines joining the origin to the points of intersection of the line sqrt3x+y=2 and the curve y^(2)-x^(2)=4 is

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

Prove that the pair of straight lines joining the origin to the points of intersection of the circles x^2+y^2=a and x^2+y^2+2(gx+fy)=0 is a^(prime)(x^2+y^2)-4(gx+fy)^2=0

If ax^2+2hxy+by^2+2gx+2fy+c=0 then find dy/dx

The product of the perpendiculars from origin to the pair of lines a x^2+2h x y+b y^2 + 2gx + 2fy + c =0 is