The circle passing through the distinct points `(1, t)`,`(t 1)` & `(t,t)` for all real values of t,passes through the point (a.b),then `a ^(2)+b^(2)` is?

The circle passing through (t,1),(1,t) and (t,t) for all values of t also passes through

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

The normal at the point (b t_(1)^(2), 2b t_(1)) on a parabola meets the parabola again in the point (b t_(2)^(2), 2b t_(2)) then

If t_(1) and t_(2) are roots of the equation t^(2)+lambda t+1=0 where lambda is an arbitrary constant.Then the line joining the points ((at_(1))^(2),2at_(1)) and (a(t_(2))^(2),2at_(2)) always passes through a fixed point then find that point.

If t_1a n dt_2 are roots of eth equation t^2+lambdat+1=0, where lambda is an arbitrary constant. Then prove that the line joining the points (a t1,22a t_1)a d n(a t2,22a t_2) always passes through a fixed point. Also, find the point.

If end points t_(1),t_(2), of a chord satisfy the relation t_(1)t_(2)=1 then chord always passes through the point if parabola is y^(2)=4x

The three distinct point A(t_(1)^(2),2t_(1)),B(t_(2)^(2),2t_(2)) and C(0,1) are collinear,if

Find the current passing through battery at t=0 and t= oo

Let normals to the parabola y^(2)=4x at variable points P(t_(1)^(2), 2t_(1)) and Q(t_(2)^(2), 2t_(2)) meet at the point R(t^(2) 2t) , then the line joining P and Q always passes through a fixed point (alpha, beta) , then the value of |alpha+beta| is equal to