Example 17 The focus of a parabolic mirror as shown in Fig 11.33 is at a distance of
5 cm from its vertex. If the mirror is 45 cm deep, find
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Ex - 18 A beam is supported at its ends by2 Fig 11.33 supports which are 12 metres apart. Since the load is concentrated at its centre, there is a deflection of 3 cm at the centre and the deflected beam is in the shape of a
parabola. How far from the centre is the deflection 1 cm? | |

Example 19 A rod AB of length 15 cm rests in between two coordinate axes in such
a way that the end point A lies on x-axis and end point B lies on
y-axis. A point P(x, y) is taken on the rod in such a way
that AP = 6 cm. Show that the locus of P is an ellipse. | |

1. If a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus.
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2. An arch is in the form of a parabola with its axis vertical. The arch is 10 m high
and 5 m wide at the base. How wide is it 2 m from the vertex of the parabola?
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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.
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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.
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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. | |

6. Find the area of the triangle formed by the lines joining the vertex of the parabola x2 = 12y to the ends of its latus rectum.
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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. | |

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