( ( A point ) ( ( ( is ( on ( the ellipse ) ) ) ( if ( ( ( the sum ) ( of ( ( the distances ) ( from ( ( that point ) ( to ( the ( two foci ) ) ) ) ) ) ) ) ( is ( equal ( to ( that ( chosen length ) ) ) ) ) ) ) ) . ) )
(ROOT (S (NP (DT A) (NN point)) (VP (VBZ is) (PP (IN on) (NP (DT the) (NN ellipse))) (SBAR (IN if) (S (NP (NP (DT the) (NN sum)) (PP (IN of) (NP (NP (DT the) (NNS distances)) (PP (IN from) (NP (NP (DT that) (NN point)) (PP (TO to) (NP (DT the) (CD two) (NNS foci)))))))) (VP (VBZ is) (ADJP (JJ equal) (PP (TO to) (NP (DT that) (VBN chosen) (NN length)))))))) (. .)))
A point is on the ellipse if the sum of the distances from that point to the two foci is equal to that chosen length.
(ROOT (S (NP (NNP Distance)) (VP (VBZ is) (NP (NP (DT the) (NN term)) (PP (IN for) (NP (NP (DT the) (NN length)) (PP (IN of) (NP (NP (DT the) (NN route)) (PP (IN between) (NP (CD two) (NNS points))))))))) (. .)))