Tangent are drawn from the point (3, 2) to the ellipse `x^2+4y^2=9` . Find the equation to their chord of contact and the middle point of this chord of contact.

Chord of contact and chord with a given middle point of parabola

Tangents are drawn from points on the line x-y+2=0 to the ellipse x^(2)+2y^(2)=4 then all the chords of contact pass through the point

Tangents are drawn to a unit circle with centre at the origin from each point on the line 2x+y=4. Then the equation to the locus of the middle point of the chord of contact is

Tangents are drawn from the points on the line x-y-5=0 to x^(2)+4y^(2)=4. Then all the chords of contact pass through a fixed point. Find the coordinates.

Tangents are drawn from the point (-1,2) to the parabola y^(2)=4x The area of the triangle for tangents and their chord of contact is

Two tangents are drawn from the point ((25)/(3),0) to the ellipse (x^(2))/(25)+(y^(2))/(16)=1 if area of the triangle formed by the tangents with the chord of contact is equal to A then find the value of A.

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.