Question 4. An arch is in the form of a semi-ellipse. It is 8 m wide and 2 m high at the center. Find the height of the arch at a point 1.5 m from one end.

Question 5. A rod of length 12 cm moves with its ends always touching the coordinate axes. Determine the equation of the locus of a point P on the rod, which is 3 cm from the end in contact with the x-axis.

Question 6. Find the area of the triangle formed by the lines joining the vertex of the parabola x^2=12y to the ends of its latus rectum.

Question 7. A man running a racecourse notes that the sum of the distances from the two flag posts from him is always 10 m and the distance between the flag posts is 8 m. Find the equation of the posts traced by the man.

Question 8. An equilateral triangle is inscribed in the parabola y^2=4ax, where one vertex is at the vertex of the parabola. Find the length of the side of the triangle.