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)

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

If the normal at the point P(x_1y_1),i=1.2,3,4 on the hyperbola xy=c^2 are concurrent at the point Q(h, k), then ((x_1+x_2+x_3+x_4)(y_1+y_2+y_3+y_4))/(x_1x_2x_3x_4) is:

The normal to the rectangular hyperbola xy = 4 at the point t_1 meets the curve again at the point t_2 Then

IF three distinct normals to the parabola y^(2)-2y=4x-9 meet at point (h,k), then prove that hgt4 .

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 normal to the rectangular hyperbola xy = 4 at the point (2t, (2)/(t_(1))) meets the curve again at (2t_(2), (2)/(t_(2))) , then

A circle cuts the rectangular hyperbola xy=1 in the points (x_(r),y_(r)), r=1,2,3,4 . Prove that x_(1)x_(2)x_(3)x_(4)=y_(1)y_(2)y_(3)y_(4)=1

If a circle and the rectangular hyperbola xy = c^(2) meet in four points 't'_(1) , 't'_(2) , 't'_(3) " and " 't'_(4) then prove that t_(1) t_(2) t_(3) t_(4) = 1 .

Ifthe normal at P to the rectangular hyperbola x^2-y^2=4 meets the axes in G and g and C is the centre of the hyperbola, then