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Let *C* be the parabola with equation *y*=4*ax*, and let *F*=(*a*,0) be
its focus.

- Let
*P*=(*x*,*y*) and*P'*=(*x'*,*y'*) be points on*C*. The area bounded by the chord*PP'*and the corresponding arc of the parabola isIt equals four-thirds of the area of the triangle

*PQP'*, where*Q*is the point on*C*whose tangent is parallel to the chord*PP'*(formula due to**Archimedes**). - The
**length**of the arc from (0,0) to the point (*x*,*y*) is - The
**polar equation**for*C*in the usual polar coordinate system isWith respect to a coordinate system with origin at

*F*the equation iswhere

*l*=2*a*is half the latus rectum. - Let
*P*be any point of*C*. Then the ray*PF*and the horizontal line through*P*make the same angle with the tangent to*C*at*P*. Thus light rays parallel to the axis and reflected in the parabola converge onto*F*(principle of the**parabolic reflector**).

*Silvio Levy
Wed Oct 4 16:41:25 PDT 1995*

This document is excerpted from the 30th Edition of the *CRC Standard Mathematical Tables and Formulas* (CRC Press). Unauthorized duplication is forbidden.