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.
Let P(at2, 2at), Q (at22, 2at2), then the pint of intersection of the tangents t1y = x + at12 and t2y = x + at22 is T(at1t2, a(t1 +t2)).
Distance of P, T and Q from y-axis, the tangent at the vertex areat2, at1t2, at22 which are G.P.
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