In the parabola `y^2=4a x ,` then tangent at `P` whose abscissa is equal to the latus rectum meets its axis at `T ,` and normal `P` cuts the curve again at `Qdot` Show that `P T: P Q=4: 5.`

In the parabola y^(2) = 4ax , the tangent at the point P, whose abscissa is equal to the latus ractum meets the axis in T & the normal at P cuts the parabola again in Q. Prove that PT : PQ = 4 : 5.

Let p be a point on the parabola y^(2)=4ax then the abscissa of p ,the ordinates of p and the latus rectum are in

If "P" is a point on the parabola " y^(2)=4ax " in which the abscissa is equal to ordinate then the equation of the normal at "P" is

Normal at P(t1) cuts the parabola at Q(t2) then relation

At a point P on the parabola y^(2) = 4ax , tangent and normal are drawn. Tangent intersects the x-axis at Q and normal intersects the curve at R such that chord PQ subtends an angle of 90^(@) at its vertex. Then

The normal at P(ct,(c )/(t)) to the hyperbola xy=c^2 meets it again at P_1 . The normal at P_1 meets the curve at P_2 =

A tangent and normal are drawn to a curve y^2=2x at A(2,2). Tangent cuts x-axis at point T and normal cuts curve again at P . Then find the value of DeltaATP

A tangent is drawn to the parabola y^2=4a x at the point P whose abscissa lies in the interval (1, 4). The maximum possible area f the triangle formed by the tangent at P , the ordinates of the point P , and the x-axis is equal to 8 (b) 16 (c) 24 (d) 32