The equation `y=(1)/(32)x^(2)` models cross sections of parabolic mirrors that are used for solar energy. There is a heating tube located at the focus of each parabola, how high is this tube located above the vertex of the parabola ?

The parabolic mirrors that are used for solar energy has the equation y=(1)/(36)x^(2) . There is a heating tube located at the focus of each parabola. How high is this tube located above the vertex of the parabola.

Find the equation of parabola whose focus is (0,1) and the directrix is x+2=0. Also find the vertex of the parabola.

Find the vertex, focus, directrix, and length of the latus rectum of the parabola x^(2)-4x-5y-1=0

Certain telescopes contain both parabolic mirror and a hyperbolic mirror. In the telescope shown in figure the parabola and hyperbola share focus F_(1) which is 14m above the vertex of the parabola. The hyperbola's second focus F_(2) is 2m above the parabola's vertex. The vertex of the hyperbolic mirror is 1m below F_(1) . Position a coordinate systemm with the origin at the centre of the hyperbola and with the foci on the y-axis. then find the equation of the hyperbola.

In each of the following find the coordinates of the focus , axis of the parabola , the equation of the directrix and the length of the latus rectum. x^(2)=6y

If the vertex of the parabola is (3,2) and directrix is 3x+4y-(19)/7=0 , then find the focus of the parabola.

A search light has a parabolic reflector (has a cross section that forms a 'bowl'). The parabolic bowl is 40 cm wide from rim to rim and 30cm deep. The bulb is located at the focus. (1) what is the equation of the parabola used for reflector? (2) How far from the vertex is the bulb to be placed so that the maximum distance covered?