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)

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)

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