The point on `y^(2)=4ax` nearest to the focus has to abscissa equal to

The point on y^(2) = 4ax nearest to the focus has its abscissa equal to

Prove that the normal chord at the point on y^(2) = 4ax , other than origin whose ordinate is equal to its abscissa subtends a right angle at the focus.

Prove that the point on the parabola y^(2) = 4ax (a gt0) nearest to the focus is its vertex.

Prove that the point on the parabola y^(2) = 4ax (a gt0) nearest to the focus is its vertex.

Find the area of the triangle formed by the lines joining the focus of the parabola y^(2) = 4x to the points on it which have abscissa equal to 16.

Find the area of the triangle formed by the lines joining the focus of the parabola y^(2) = 4x to the points on it which have abscissa equal to 16.

Prove that the point on the parabola y^(2) = 4a ( a gt 0 nearest to the focus is its vertex.

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.

The normal chord of y^(2)=4ax at a point where abscissa is equal to ordinate subtends at the focus an angle theta