In the parabola `y^(2)=4ax`, the tangent at P whose abscissa is equal to the latus rectum meets its axis at T, and normal at P cuts the curve again at Q. Show that PT : PQ = 4 : 5.

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.

The parabola y^2=4ax passes through the point (2,-6). Find the length of the latus rectum.

If the normals to the parabola y^2=4a x at the ends of the latus rectum meet the parabola at Qa n dQ^(prime), then Q Q ' is

If a normal to a parabola y^2 =4ax makes an angle phi with its axis, then it will cut the curve again at an angle

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

If focal distance of a point P on the parabola y^(2)=4ax whose abscissa is 5 10, then find the value of a.

Foot of perpendicular from point P on the parabola y^(2)=4ax to the axis is N. A straight line is drawn parallel to the axis which bisects PN and cuts the curve at Q. If NQ meets the tangent at the vertex A at a point T, then (PN)/(AT) =__________.

If the tangent t the curv y=f(x )"at" P(x_(1),y_(1)) is paralle to the y-axis, then the of the normal to the curve at P is -

If the tangents at the points Pa n dQ on the parabola y^2=4a x meet at T ,a n dS is its focus, the prove that S P ,S T ,a n dS Q are in GP.

Let S is the focus of the parabola y^2 = 4ax and X the foot of the directrix, PP' is a double ordinate of the curve and PX meets the curve again in Q. Prove that P'Q passes through focus.