4. Parabolas have an interesting property. If a parabolic reflector receives lig

Question

4. Parabolas have an interesting property. If a parabolic reflector receives light (or sound waves, for example) entering the reflector parallel to the axis of symmetry, then all that light or sound is concentrated to the focus. In three dimensions, that location is a great place to put a microphone (or light source if you want to have a spotlight!). Suppose you wanted to create a HUGE parabolic dish that would be 80 feet wide. The depth of the dish would be 1 2 feet. Q: Where is the focus? As an interesting apllication, you can buy a solar cigarette lighter from amazon.com for $7.04 plus shipping! Bonus: If the solar cigarette lighter is 4 inches across and 1/4 inch deep, then where is the focus? Solar Spark Cigarette Lighter

Explanation / Answer

since the parabolic dish is 80 feet wide, that must be its latus rectum ,and considering the base to be origin the depth of the parabola will be its focus.so if base is at 0,0 then focus is at (12,0)

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