For what values of the parameter `t` does the point `P (t,t + 1)` lies inside the triangle `ABC` where `A = (0,3), B= (-2,0) and C= (6,1).`

Find lambda if (lambda, lambda +1) is an interior point of Delta ABC where, A-=(0,3), B-= (-2,0) and C -= (6, 1) .

Find the absolute value of parameter t for which the area of the triangle whose vertices the A(-1,1,2);B(1,2,3) and C(t,1,1) is minimum.

The locus of the point (a+bt,b-(a)/(t)) where t is the parameter is

The point (1,t) lies inside the circle through the points (2,3),(2,4) and (0,5) if r does not lie in the interval

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 P(t ) = t^2 - 1 , find the value of P(1) , P(-1), P(0), P(-2)

Let A ( 1, 0 ) , B ( 6, 2 ) and C (( 3 ) /(2), 6 ) be the vertices of a triangle ABC. If P is a point inside the triangle ABC such that the triangles APC, APB and BPC have equal areas , then the length of the line segment PQ, where Q is the point ( - ( 7 ) /(6), - ( 1 ) /(3)) , is _________.