Show that the locus of point from which tan- gents one each to `y^(2) = 4a(x+ a)` and `y^(2) =` 4b(x+b) are at right angles is x+a+b=0.

Show that the locus of point of intersection of perpendicular tangents to the parabola y(2)=4ax is the directrix x+a=0.

If two tangents drawn from a point P to the parabola y^(2)=4x are at right angles then the locus of P is

Find the locus of midpoint of chords of the circle x ^(2) + y ^(2) = r^(2) , substending a right angle at the point (a,b)

Show that the curves y^(2)=4a(x+a) and y^(2)=4b(b-x)(a gt ,b gt 0) intresect orthogonally.

The locus of the point from which the length of the tangent to the circle x^(2)+y^(2)-2x-4y+4=0 is 3 units is

The locus of the point which is such that the lengths of the tangents from it to the circles x^(2)+y^(2)=a^(2) and x^(2)+y^(2)=b^(2) are inversely as their radii is