From points on the circle `x^2+y^2=a^2` tangents are drawn to the hyperbola `x^2-y^2=a^2`. Then, the locus of mid-points of the chord of contact of tangents is:

From the points on the circle x^(2)+y^(2)=a^(2) , tangents are drawn to the hyperbola x^(2)-y^(2)=a^(2) : prove that the locus of the middle-points (x^(2)-y^(2))^(2)=a^(2)(x^(2)+y^(2))

From a point on the line x-y+2-0 tangents are drawn to the hyperbola (x^(2))/(6)-(y^(2))/(2)=1 such that the chord of contact passes through a fixed point (lambda, mu) . Then, mu-lambda is equal to

From (3,4) chords are drawn to the circle x^(2)+y^(2)-4x=0. The locus of the mid points of the chords is :

Tangents are drawn to the parabola y^(2)=4x from the point (1,3). The length of chord of contact is

If the angle between the tangents at the end points of the chords of the hyperbola (x^(2))/(9)-(y^(2))/(4)=1 is 90 then the locus of mid point of the chord of contact is

Statement 1 : If from any point P(x_1, y_1) on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=-1 , tangents are drawn to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1, then the corresponding chord of contact lies on an other branch of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=-1 Statement 2 : From any point outside the hyperbola, two tangents can be drawn to the hyperbola.

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.