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= $\displaystyle 4$, the vertex is $\displaystyle (-2,0)$ and the equation of the axis is $\displaystyle 3x+4y+6=0$ then find the equation of a parabola satisfying these. (Ans: $\displaystyle 9x^2+24xy+16y^2-44x+108y-124=0,\

9x^2+24xy+16y^2+36x+48y+108=0$)

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)