Show that the locus of points from which the tangents drawn to a circle are orthogonal, is a concentric circle. Or Find the equation of the director circle of the circle `x^2 + y^2 = a^2`.

the equation to the director circle of (x^2)/6+(y^2)/4=1 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 the point of intersection of the two tangents drawn to the circle x^2 + y^2=a^2 which include are angle alpha is

The line 5x - y = 3 is a tangent to a circle at the point (2, 7) and its centre is on theline x + 2y = 19 . Find the equation of the circle.

Find the equations of the tangents to the circle x^(2) + y^(2)=16 drawn from the point (1,4).

The angle between the tangents drawn from a point on the director circle x^(2)+y^(2)=50 to the circle x^(2)+y^(2)=25 , is

Show that if the length of the tangent from a point P to the circle x^2 + y^2 = a^2 be four times the length of the tangent from it to the circle (x-a)^2 + y^2 = a^2 , then P lies on the circle 15x^2 + 15y^2 - 32ax + a^2=0 .

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

Find the equation of the circle concentric with the circle 2x^2 + 2y^2 - 6x + 8y+1=0 and of double its area.

Show that the angle between the tangents drawn from (-1,3) to the circle x^(2)+y^(2)=5 is 90^(@) .