Chord of contact from a point

Find the equation of the chord of contact of the point (3,1) to the ellipse x^2+9y^2=9 . Also find the mid-point of this chord of contact.

Find the equation of the chord of contact of the point (5, 1) to the hyperbola, x^(2) - 4y^(2) = 16 . Also find the mid-point of this chord.

Perpendiculars are drawn,respectively,from the points P and Q to the chords of contact of the points Q and P with respect to a circle. Prove that the ratio of the length of perpendiculars is equal to the ratio of the distances of the points P and Q from the center of the circles.

The length of chord of contact of the point (3,6) with respect to the circle x^(2)+y^(2)=10 is

Length of the chord of contact drawn from the point (-3,2) to the parabola y^(2)=4x is

Chord of contact of tangents drawn from the point M(h, k) to the ellipse x^(2) + 4y^(2) = 4 intersects at P and Q, subtends a right angle of the centre theta