Tangent Are Drawn To A Parabola From A Point T. If P, Q are The Points Of Constant Then Perpendicular Distance From P, T and Q upon The Tangent At The Vertex Of The Parabola Are In.

The locus of the mid-point of the line segment joining the focus to a moving point on the parabola y² = 4ax is another parabola with directrix

Equation of a common tangent to the curves y² = 8x and xy = –1 is 

The tangent at the point P(x₁, y₁) to the parabola y² = 4ax meets the parabola y² = 4a(x + b) at Q and R, the coordinates of the mid-point of QR are  

Consider a parabola y² = 4ax, the length of focal chord is l and the length of the perpendicular from vertex to the chord is pthen

Chord of the parabola  which subtend right angle at vertex pass through

The locus of the vertex of the family of parabolas   is