Tangent and normal drawn to a parabola at `A(a t^2,2a t),t!=0` meet the x-axis at point `B` and `D` , respectively. If the rectangle `A B C D` is completed, then the locus of `C` is
`(a)y=2a` (b) `y+2a=c` `(c)x=2a` (d) none of these

Tangents and normal drawn to the parabola y^2=4a x at point P(a t^2,2a t),t!=0, meet the x-axis at point Ta n dN , respectively. If S is the focus of theparabola, then (a) S P=S T!=S N (b) S P!=S T=S N (c) S P=S T=S N (d) S P!=S T!=S N

If a tangent to the parabola y^(2) = 4ax meets the x-axis in T and the tangent at the Vertex A in P and the rectangle TAPQ is completed then locus of Q is

If a tangent to the parabola y^2=4a x meets the x-axis at T and intersects the tangents at vertex A at P , and rectangle T A P Q is completed, then find the locus of point Qdot

If a tangent to the parabola y^2=4a x meets the x-axis at T and intersects the tangents at vertex A at P , and rectangle T A P Q is completed, then find the locus of point Qdot

If a tangent to the parabola y^2 = 4ax meets the axis of the parabola in T and the tangent at the vertex A in Y, and the rectangle TAYG is completed, show that the locus of G is y^2 + ax = 0.

If the tangent drawn to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 at any point P meets the coordinate axes at the points A and B respectively. If the rectangle OACB (O being the origin) is completed, where C lies on (x^2)/(a^2)-(y^2)/(b^2)=lambda . Then, the value of lambda is:

The tangent and the normal at the point A-= (4, 4) to the parabola y^2 = 4x , intersect the x-axis at the point B and C respectively. The equation to the circumcircle of DeltaABC is (A) x^2 + y^2 - 4x - 6y=0 (B) x^2 + y^2 - 4x + 6y = 0 (C) x^2 + y^2 + 4x - 6y = 0 (D) none of these

Suppose a parabola y = x^(2) - ax-1 intersects the coordinate axes at three points A,B and C, respectively. The circumcircle of DeltaABC intersects the y-axis again at the point D(0,t) . Then the value of t is

If the normals at points t_1 and t_2 meet on the parabola, then (a) t_1t_2=1 (b) t_2=-t_1-2/(t_1) (c) t_1t_2=2 (d) none of these

If A=[(5,x),( y,0)] and A=A^T , then a) x=0,\ \ y=5 (b) x+y=5 (c) x=y (d) none of these