The locus of the vertex of the family of parabolas is
Equation of the parabola is
whose vertex 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
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.
Chord of the parabola which subtend right angle at vertex pass through