On the parabola `y^(2)=4ax, P` is the point with parameter t,Q is the opposite xtremity of the focal chord through P and R is the point for which QR is paralle to PK where K is the point (2a,0). Show that R has parameter `(t^(2)-1)/(t)`.

If the point P(4, -2) is the one end of the focal chord PQ of the parabola y^(2)=x, then the slope of the tangent at Q, is

Find the points of contact Q and R of a tangent from the point P(2,3) on the parabola y^2=4xdot

If the tangent at any point P to the parabola y^(2)=4ax meets the directrix at the point K , then the angle which KP subtends at its focus is-

The locus of the middle points of the focal chords of the parabola, y^2=4x is:

If t is parameter then the locus of the point P(t,(1)/(2t)) is _

Let a, r, s, t be non-zero real numbers. Let P(at^(2),2at),Q(ar^(2),2ar)andS(as^(2),2as) be distinct points on the parabola y^(2)=4ax . Suppose that PQ is the focal chord and lines QR and PK are parallel, where K the point (2a,0). If st=1, then the tangent at P and the normal at S to the parabola meet at a point whose ordinate is

Let a, r, s, t be non-zero real numbers. Let P(at^2, 2at), Q, R(ar^2, 2ar) and S(as^2, 2as) be distinct points onthe parabola y^2 = 4ax . Suppose that PQ is the focal chord and lines QR and PK are parallel, where K isthe point (2a, 0). The value of r is

If the angle between the normal to the parabola y^(2)=4ax at point P and the focal chord passing through P is 60^(@) , then find the slope of the tangent at point P.

If the normal to the parabola y^2=4a x at point t_1 cuts the parabola again at point t_2 , then prove that t_2^2 geq8.

If normals drawn at three different point on the parabola y^(2)=4ax pass through the point (h,k), then show that hgt2a .