The equation of the chord of contact of the point (1, -2) w.r.t the ellipse `4x^(2)+5y^(2)=20` is

The equation of the chord of contact of the point (3,-2) w.r.t. the hyperbola 2x^(2) -3y^(2) =12 is

The equation of the polar of the point (2, -1) w.r.t the ellipse 3x^(2)+4y^(2)=12 is

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.

The equation of the chord of contact of the point (4,2) with respect to the circle x^(2)+y^(2)-5x+4y-3=0 is

The condition that the chord of contact of the point (b,c) w.r.t. to the circle x^(2)+y^(2)=a^(2) should substend a right angled at the centre is

The pole of the line 2x-y+2=0 w.r.t the ellipse 3x^(2)+5y^(2)=15 is

Let AB be chord of contact of the point (5,-5) w.r.t the circle x^(2)+y^(2)=5. Then find the locus of the orthocentre of the triangle PAB, where P is any point moving on the circle.

The chord of contact of (2,1) w.r.t to the circle x^(2)+y^(2)+4x+4y+1=0 is