If a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus.
Focus is at the mid-point of the given diameter.
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?
2.23 m (approx.)
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.
9.11 m (approx.)
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.
1.56 m (approx.)
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.
\( \dfrac{x^2}{81} + \dfrac{y^2}{9} = 1 \)
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.
18 sq units
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.
\( \dfrac{x^2}{25} + \dfrac{y^2}{9} = 1 \)
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.
\( 8\sqrt{3}a \)