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)]`.

If the normals at (x_(i),y_(i)) i=1,2,3,4 to the rectangular hyperbola xy=2 meet at the point (3,4) then

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

If the normals at four points P (x_i y_i), i = 1, 2, 3, 4 on the rectangular hyperbola xy = c^2 , meet at the point Q(h, k), then prove that x_1 + x_2 + x_3 + x_4 =h

If the normal at four points P_(i)(x_(i), (y_(i)) l, I = 1, 2, 3, 4 on the rectangular hyperbola xy = c^(2) meet at the point Q(h, k), prove that x_(1) + x_(2) + x_(3) + x_(4) = h, y_(1) + y_(2) + y_(3) + y_(4) = k x_(1)x_(2)x_(3)x_(4) =y_(1)y_(2)y_(3)y_(4) =-c^(4)

Show that the equation of the chord joining two points (x_(1),y_(1)) and (x_(2),y_(2)) on the rectangular hyperbola xy=c^(2) is (x)/(x_(1)+x_(2)) +(y)/(y_(1)+y_(2))=1

Tangents are drawn from the point P(1,-1) to the circle x^2+y^2-4x-6y-3=0 with centre C, A and B are the points of contact. Which of the following are correct?

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.

Find the common tangent of y=1+x^(2) and x^(2)+y-1=0 . Also find their point of contact.

If the normals at two points (x_(1),y_(1)) and (x_(2),y_(2)) of the parabola y^(2)=4x meets again on the parabola, where x_(1)+x_(2)=8 then |y_(1)-y_(2)| is equal to