Chord of Contact

Find the locus of the middle points of the chords of contact of orthogonal tangents of the parabola y^(2)=4ax .

If a chord of contact of tangents drawn from a point P with respect to the circle x^(2)+y^(2)=9 is x=2, then area, in square units, of triangle formed by tangents drawn from P to the circle and their chord of contact is equal to

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.

The chords of contact of all points on a line w.r.t the parabola y^(2)=4x are concurrent at the point (1,0) .The equation of the line

The chords of contact of Pwrt.x^(2)-y^(2)=a^(2) and x^(2)+y^(2)=a^(2) are at right angles.The locus of P is

If the chords of contact of tangents drawn from P to the hyperbola x^(2)-y^(2)=a^(2) and its auxiliary circle are at right angle, then P lies on

Statement-1: The line x+9y-12=0 is the chord of contact of tangents drawn from a point P to the circle 2x^(2)+2y^(2)-3x+5y-7=0 . Statement-2: The line segment joining the points of contacts of the tangents drawn from an external point P to a circle is the chord of contact of tangents drawn from P with respect to the given circle

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.