From the point `(x_1, y_1) and (x_2, y_2)`, tangents are drawn to the rectangular hyperbola `xy=c^(2)`. If the conic passing through the two given points and the four points of contact is a circle, then show that `x_1x_2=y_1y_2 and x_1y_2+x_2y_1=4c^(2)`.

Tangent are drawn from two points (x_1, y_1) and (x_2, y_2) to xy = c^2 . The conic passing through the two points and through the four points of contact will be circle if (A) x_1 x_2 = y_1 y_2 (B) x_1 y_2 = x_2 y_1 (C) x_1 y_2 + x_2 y_1 = 4c^2 (D) x_1 x_1 + y_1 y_2 = 4c^2

Tangents are drawn from the points (x_(1), y_(1))" and " (x_(2), y_(2)) to the rectanguler hyperbola xy = c^(2) . The normals at the points of contact meet at the point (h, k) . Prove that h [1/x_(1) + 1/x_(2)] = k [1/y_(1)+ 1/y_(2)] .

Tangents are drawn from any point on the hyperbola (x^2)/9-(y^2)/4=1 to the circle x^2+y^2=9 . Find the locus of the midpoint of the chord of contact.

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

If P(x_1,y_1),Q(x_2,y_2),R(x_3,y_3) and S(x_4,y_4) are four concyclic points on the rectangular hyperbola ) and xy = c^2 , then coordinates of the orthocentre ofthe triangle PQR is

If P(x_1,y_1),Q(x_2,y_2),R(x_3,y_3) and S(x_4,y_4) are four concyclic points on the rectangular hyperbola ) and xy = c^2 , then coordinates of the orthocentre ofthe triangle PQR is

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

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

Tangents AB and AC are drawn to the circle x^(2)+y^(2)-2x+4y+1=0 from A(0,1) then equation of circle passing through A,B and C is

From a point on the line y=x+c , c(parameter), tangents are drawn to the hyperbola (x^(2))/(2)-(y^(2))/(1)=1 such that chords of contact pass through a fixed point (x_1, y_1) . Then , (x_1)/(y_1) is equal to