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

A point on the line x=4 from which the tangents drawn to the circle 2(x^(2)+y^(2))=25 are at right angles, is

A point on the line x=3 from which the tangents drawn to the circle x^2+y^2=8 are at right angles is

The locus of a point from which two tangent are drawn to x^2-y^2=a^2 which are inclined at angle (pi)/(4) to each other is

The locus of a point from which two tangent are drawn to x^2-y^2=a^2 which are inclined at angle (pi)/(4) to each other is

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

Show that the area included between the parabolas y^2 = 4a(x + a) and y^2 = 4b(b - x) is 8/3 sqrt(ab) (a+b).

The locus of the point of intersection of tangents to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 which meet at right , is

The locus of the point of intersection of tangents to the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 , which make complementary angles with x - axis, is

Find the locus of the points of the intersection of tangents to ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 which make an angle theta.

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