Conic Sections Parabola Ellipse Parabola A set of points in from fixed point F called the Directrix a Hyperbola plane that called a Focus are equidistant and a fixed line Turning point called vertex Deriving equation For y open vertex p n p y p up y k a h aply k y k Focus directrix h shyfts h 4p a h k Directrix h p K P y 14 up a Focus h p k Directrix x h p Notes mm V pro n pro Ak y upx Noteim If only Similarly proven a vy is squared then parabola LI n.T all mo of symmetry yess Meggie a of symmetry Etyn anonymity if t.is tIii1 if Gas Ellipses An ellipse is a set of points in the plane 2 fixed points Fi n Fe is distances from 2 Fixed points called Foci Play b get co vertical 1 PF.lt PF2 3 From with origin 29 Δ F EP 229 2 C Ca 4 let semi major axis major radius b semi minor axis minor radius midpt 0,0 c o y axis c ca a c 2 azb a2 b c c a n b an o 1a o vertices vertices a'b 1 azbso 1 where ay x 22 1 where so at c b then b a Foci on x axis C 3 minor axis skinny foci o x axis in middle major axis bree Foci on of whose constant a foci on 1 Place b foci sum Steps a a the o Ial Hyperbola The set of all points distances from in a the plane fixed points Fi n Fz 2 difference of whose the foci is a constant PF PFal 129 P ny.fr s Eht a play Tt radio where ca4b vertices 19,0 Foci C 0 Note when drawing 22 Wen acc but always under 0 doe one with a is term TE Y 4 1 major access gpoint 23 Foci 2 start with asymtotes faint c c vertices Asymptotes Nue if where a lab z b o az b ME a y a 9 1 h y k assymtotes will a Foci o c where vertices o a asymptotes y intersect h k nv c b In be are