The tangent and normal at the point `P(4,4)` to the parabola, `y^(2) = 4x` intersect the x-axis at the points Q and R, respectively. Then the circumcentre of the `DeltaPQR` is

Prove that the normals at the points (1,2) and (4,4) of the parabola y^(2)=4x intersect on the parabola

Prove that the normals at the points (1,2) and (4,4) of the parbola y^(2)=4x intersect on the parabola.

A tangent and a normal are drawn at the point P(2,-4) on the parabola y^(2)=8x , which meet the directrix of the parabola at the points A and B respectively. If Q (a,b) is a point such that AQBP is a square , then 2a+b is equal to :

Tangent and normal at any point P of the parabola y^(2)=4ax(a gt 0) meet the x-axis at T and N respectively. If the lengths of sub-tangent and sub-normal at this point are equal, then the area of DeltaPTN is given by

Tangent and normal at any point P of the parabola y^(2)=4ax(a gt 0) meet the x-axis at T and N respectively. If the lengths of sub-tangent and sub-normal at this point are equal, then the area of DeltaPTN is given by

If the normals at two points P and Q of a parabola y^2 = 4ax intersect at a third point R on the curve, then the product of ordinates of P and Q is