The circle passing through the points (1, t), (t, 1) and (t, t) for all values of t passes through the point

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

If t_1 a n d t_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 t1^2,2a t_1)a d n(a t2^2,2a t_2) always passes through a fixed point. Also, find the point.

If t_1 a n d t_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.

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

If t_1 and t_2 are the roots of the equation t^2+lambdat+1=0 ,where lambda is an orbitary constant,then prove that the line joining the point (at_1^2,2at_1) and (at_2^2,2at_2) always passes through a fixed point.Also find that point.

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.

A tangent to the ellipse 4x^2 +9y^2 =36 is cut by the tangent at the extremities of the major axis at T and T^1 , the circle on T T^1 as diameter passes through the point

A tangent to the ellipse 4x^2 +9y^2 =36 is cut by the tangent at the extremities of the major axis at T and T^1 , the circle on T T^1 as diameter passes through the point

Find Distance between the points for which lines that pass through the point (1, 1) and are tangent to the curve represent parametrically as x = 2t-t^2 and y = t + t^2