8. An equilateral triangle is inscribed in the parabola , where one vertex is at the vertex of the parabola. Find the length of the side of the triangle.
6. Find the area of the triangle formed by the lines joining the vertex of the parabola to the ends of its latus rectum.
6. 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.
4. An arch is in the form of a semi-ellipse. It is 8 m wide and 2 m high at the centre. Find the height of the arch at a point 1.5 m from one end.
3. The cable of a uniformly loaded suspension bridge hangs in the form of a parabola. The roadway which is horizontal and 100 m long is supported by vertical wires attached to the cable, the longest wire being 30 m and the shortest being 6 m Find the length of a supporting wire attached to the roadway 18 m from the middle
1. If a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus.