If a circle cuts a rectangular hyperbola xy=1 in four points P,Q,R,S and the parameters of these four points be `t_(1),t_(2),t_(3) and t_(4)` respectively and `-20t_(1)t_(2)t_(3)t_(4)=k`, then value of k equals

Points A,B,C,D, on y^(2) = 4ax have parameters t_(1) , t_(2), t_(3) , t_(4) respectively . If AB bot CD then (t_(1) + t_(2)) (t_(3) + t_(4)) =

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 .

A circle drawn on any focal AB of the parabola y^(2)=4ax as diameter cute the parabola again at C and D. If the parameters of the points A, B, C, D be t_(1), t_(2), t_(3)" and "t_(4) respectively, then the value of t_(3),t_(4) , 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 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

Statement :1 If a parabola y ^(2) = 4ax intersects a circle in three co-normal points then the circle also passes through the vertr of the parabola. Because Statement : 2 If the parabola intersects circle in four points t _(1), t_(2), t_(3) and t_(4) then t _(1) + t_(2) + t_(3) +t_(4) =0 and for co-normal points t _(1), t_(2) , t_(3) we have t_(1)+t_(2) +t_(3)=0.

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

Points A,B ,C , D on y^(2) = 4ax have parameters t_(1) , t_(2), t_(3), t_(4) respectively . If AB || CD , then

Find the locus of the point (t^(2)-t+1,t^(2)+t+1),t in R