Prove that any three tangents to a parabola whose slopes are in harmonic progression enclose a triangle of constant area.

In Delta ABC, sec A, sec B, sec C are in harmonic progression, then

If P, Q, R are three points on a parabola y^2=4ax whose ordinates are in geometrical progression, then the tangents at P and R meet on :

Prove that the tangent at any point on the rectangular hyperbola xy = c^2 , makes a triangle of constant area with coordinate axes.

Find the locus of the point of intersection of two tangents to the parabola y^(2)=4ax , which with the tangent at the vertex forms a triangle of constant area 4sq. units.

If three real numbers a,b and c are in harmonic progression, then which of the folllowing is true ?

Tangents are drawn to the parabola at three distinct points.Prove that these tangent lines always make a triangle and that the locus of the orthocentre of the triangle is the directrix of the parabola.