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Prove that the least focal chord of a pa...

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

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

Prove that the least focal chord of a parabolaa is it rectum.

Q is any point on the parabola y^(2) =4ax ,QN is the ordinate of Q and P is the mid-point of QN ,. Prove that the locus of p is a parabola whose latus rectum is one -fourth that of the given parabola.

Find the equation of the parabola whose vertex is (2,3) and the equation of latus rectum is x = 4 . Find the coordinates of the point of intersection of this parabola with its latus rectum .

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

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

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

Statement - I : The all chords passing through focus of an ellipse , the latus rectum will be the minimum in length . Statement - II : The sum of the reciprocals of the segments of any focal chord of an ellipse Is half of latus rectum .

If the focus of a parabola is (2, 3) and its latus rectum is 8, then find the locus of the vertex of the parabola.

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.