1.Prove that the orthocentre of the triangle formed by the three tangents to a parabola lie on a directrix.

2.If the Latus Rectum= , the vertex is and the equation of the axis is then find the equation of a parabola satisfying these. (Ans: )

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

Kindly please help in the above questions. Any thoughts or hints would be highly appreciated. Thank you. (Happy)

Question 3 has been solved. Thanks to Soroban! (Happy)