Angle between tangents drawn from a point `P` to circle `x^2 + y^2 -48 - 8y + 8 = 0` is `60^@` then length of chord of contact of `P` is

The angle between tangents drawn from a point P to the circle x^2+y^2+4x-2y-4=0 is 60^@ Then locus of P is

Pair of tangents are drawn from origin to the circle x^2 + y^2 – 8x – 4y + 16 = 0 then square of length of chord of contact is

If angle between two tangents drawn from a point P to a circle of radius a and centre 0 is 60^(@) then OP=asqrt3 .

If the pair of tangents are drawn from the point (4,5) to the circle x^(2)+y^(2)-4x-2y-11=0 , then (i) Find the length of chord of contact. (ii) Find the area of the triangle fromed by a pair of tangents and their chord of contact. (iii) Find the angle between the pair of tangents.

Find the area of the quadrilateral formed by common tangents drawn from a point P to the circle x^(2) + y^(2) = 8 and the parabola y^(2) =16x , chord of contact of tangents to the circle and chord of contact of tangents to the parabolas.

The angle between the tangents drawn from the point (2, 6) to the parabola y^(2)-4y-4x+8=0 is

Length of a tangent drawn from the origin to the circle x ^(2) + y ^(2) - 6x + 4y + 8=0 in units is

The angle between a pair of tangents from a point P to the circle x^(2)+y^(2)-6x-8y+9=0 is (pi)/(3) . Find the equation of the locus of the point P.

The angle between a pair of tangents from a point P to the circle x^(2)+y^(2)=25 is (pi)/(3). Find the equation of the locus of the point P .