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`.

If the normal at (ct,c/t) on the curve xy=c^2 meets the curve again in 't' , then :

If the normal at the point t_(1) to the rectangle hyperola xy=c^(2) meets it again at the point t_(2) prove that t_(1)^(3) t_(2)=-1

if the normal at the point t_(1) on the parabola y^(2) = 4ax meets the parabola again in the point t_(2) then prove that t_(2) = - ( t_(1) + 2/t_(1))

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 .

Show that the normal at the point (3t,(4)/(t)) to the curve xy=12 cuts the curve again at the point whose parameter t_(1) is given by t_(1)=-(16)/(9t^(3))

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

The normal at a point t_1 on y^2 = 4ax meets the parabola again in the point t_2 . Then prove that t_1 t_2 + t_1^2 + 2=0

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