Show that the normal to the rectangular hyperbola `xy = c^(2)` at the point t meets the curve again at a point t' such that `t^(3)t' = - 1`.

If the normal to the rectangular hyperbola xy=c^(2) at the point t' meets the curve again at t_(1) then t^(3)t_(1), has the value equal to

The normal to the rectangular hyperbola xy=4 at the point t_(1), meets the curve again at the point t_(2) Then the value of t_(1)^(2)t_(2) is

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

If the normal at point 't' of the curve xy = c^(2) meets the curve again at point 't'_(1) , then prove that t^(3)* t_(1) =- 1 .

The normal to curve xy=4 at the point (1, 4) meets curve again at :

If the normal to the parabola y^(2)=4ax at point t_(1) cuts the parabola again at point t_(2) then prove that t_(2)^(2)>=8

If the normal to the given hyperbola at the point (c t , c/t) meets the curve again at (c t^(prime), c/t^(prime)), then (A) t^3t^(prime)=1 (B) t^3t^(prime)=-1 (C) t t^(prime)=1 (D) t t^(prime)=-1

Normal equation to the curve y^(2)=x^3 at the point (t^(2),t^(3)) on the curve is

The tangent to the curve y=x^(3) at the point P(t, t^(3)) cuts the curve again at point Q. Then, the coordinates of Q are