val ▁ ▁can ▁be ▁described ▁by ▁a ▁function ▁ ▁such ▁that : ▁ ▁The ▁tang ent ▁at ▁point ▁ ▁will ▁be ▁described ▁using ▁a ▁function ▁ ▁such ▁that ▁its ▁equation ▁is ▁▁ ▁Hence ▁( s . ▁image ) ▁ ▁and ▁▁ ▁I : ▁if ▁ ▁is ▁a ▁non ▁deg ener ate ▁con ic ▁we ▁have ▁ ▁and ▁ ▁and ▁one ▁calcul ates ▁easily ▁that ▁ ▁are ▁col linear . ▁ ▁II : ▁If ▁ ▁is ▁an ▁o val ▁with ▁property ▁( P 3 ), ▁the ▁slope ▁of ▁the ▁line ▁ ▁is ▁equal ▁to ▁the ▁slope ▁of ▁the ▁line ▁, ▁that ▁means : ▁ ▁and ▁hence ▁( i ): ▁ ▁for ▁all ▁ ▁. ▁ ▁With ▁▁ ▁one ▁gets ▁( ii ): ▁ ▁and ▁from ▁ ▁we ▁get ▁ ▁( iii ): ▁▁ ▁( i ) ▁and ▁( ii ) ▁yield ▁( iv ): ▁ ▁and ▁with ▁( iii ) ▁at ▁least ▁we ▁get ▁ ▁( v ): ▁ ▁for ▁all ▁. ▁ ▁A ▁consequence ▁of ▁( ii ) ▁and ▁( v ) ▁is ▁▁▁ ▁. ▁ ▁Hence ▁ ▁is ▁a ▁non de generate ▁con ic . ▁ ▁Rem ark : ▁Property ▁( P 3 ) ▁is ▁ful filled ▁for ▁any ▁o val ▁in ▁a ▁p app ian ▁project ive ▁plane ▁of ▁characteristic ▁ 2 ▁with ▁a ▁nucle us ▁( all ▁tang ents ▁meet ▁at ▁the ▁nucle us ). ▁Hence ▁in ▁this ▁case ▁( P 3 ) ▁is ▁also ▁true ▁for ▁non - con ic ▁o val s . ▁ ▁Seg re ' s