Most traditional reference books say that the focus of the parabola f[x] = x^2/(

Question

Most traditional reference books say that the focus of the parabola f[x] = x^2/(4 p) is located at the point {0, p} on the vertical-axis. Why do they say this? Why do folks use parabolas to build television satellite dish antennas to sell to rednecks in the boonies who want to watch wrestling and roller derby? The great Greek scientist, Archimedes (287-212 B.C.), was the first scientist to understand what parabolic mirrors can do. In fact, Archimedes once used parabolic mirrors to concentrate sunlight on the sails of attacking Roman ships, thereby burning them up before they could attack. How do you think Archimedes went about this?

Explanation / Answer

from the given question,

f[x] = x^2/(4 p)

x2=4py

(x-0)2=4p(y-0)

This is in the standard form of parabola whose axis is vertical is

(x-h)2=4a(y-k)

where (h,k) is vertex and a is focus from vertex.

as a=p, the focus lies on (0,p)

the beam of rays incident on a parabolic surface, reflect to a single point.

Hence the antennas are parabolic.

similarly, suns beam of light are parallel. if they are incident on parabolic mirrors, they all reflect on focus. Thus Archimedes was able to burn roman ship, by reflecting parallel beam of light at a single point.

Related Questions

Navigate

• Browse (All)
• Browse M
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.