Show that the circle described on a focal chord of a parabola as diameter touches its directrix .

Prove that the least focal chord of a parabola is its latus rectum .

Prove that the least focal chord of a parabola is the latus rectum .

Prove that the normal at the extermities of a focal chord of a parabola intersect at right angles.

Show that the sum of the reciprocals of the segments of any focal chord of a parabola y^2=4ax is constant.

Prove that the sum of the reciprocals of the segments of any focal chord of a parabola is constant .

Show that the product of the ordinates of the ends of a focal chord of the parabola y^(2) = 4ax is constant .

Prove that the line joining the orthocentre to the centroid of a triangle formed by the focal chord of a parabola and tangents drawn at its extremities is parallel to the axis of the parabola.

Show that the equation of the circle described on the chord x cos alpha + y sin alpha = p of the circle x^(2) + y^(2) = a^(2) as diameter is x^(2) + y^(2) - a^(2) - 2p (x cos alpha + y sin alpha - p) = 0

Consider a circle with its centre lying on the focus of the parabola, y^2=2px such that it touches the directrix of the parabola. Then a point of intersection of the circle & the parabola is:

State true or false . The longest of all chords of a circle is called a diameter.