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

If the normal chord drawn at the point t to the parabola y^(2) = 4ax subtends a right angle at the focus, then show that ,t = pmsqrt2

Find the point P on the curve y^(2)= 4ax which is nearest to the point (11a, 0)

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

Prove that the tangents drawn on the parabola y^(2)=4ax at points x = a intersect at right angle.

The focus of the parabola y^(2)-4y-8x-4=0 is

If a normal chord at a point on the parabola y^(2)=4ax subtends a right angle at the vertex, then t equals

Prove that the locus of the foot of the perpendicular drawn from the focus of the parabola y ^(2) = 4 ax upon any tangent to its is the tangent at the vertex.

If the tangents at the points P and Q on the parabola y^2 = 4ax meet at R and S is its focus, prove that SR^2 = SP.SQ .

Prove that the equation of the parabola whose focus is (0, 0) and tangent at the vertex is x-y+1 = 0 is x^2 + y^2 + 2xy - 4x + 4y - 4=0 .

The vertex or the parabola y = ax^(2)+bx+c is