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Parabola, Ellipse, and Hyperbola yearning Objectives atthe course of this chapter, you will be able to: ya. Identify the three main forms of a Parabolic . 14-4, understand to locate a hyperbola’s vertices equation and foci 14-2, Use concepts of vertex, axis of symmetry and 14-5 . learn to graph hyperbolas not centered at the intercept as they relate to parabolas. origin. 143. learn to graph an ellipse in standard form and determine the equation of an ellipse by its graph. UAB GEclr EY . 3 (P+ mL @- ph + - gy] | . =e (e+ my t+np Aconi¢ section, or conic, is the locus of a point which moves ; inaplane so that its distance from a fixed point is ina constant Sart 2hry + by + 2gx + 2p te mio to its perpendicular distance from a fixed straight line, =0. 1, The fixed point is called the focus. : . a. 2. The fixed straight line is called the directrix. icnted Distinguishing between 3 jo i ntricity denote . ise mame mio Inealled We iecrento LL | | 4. The line passing through the focus and perpendicular The nature of the conic section depends upon the position | _ tothe directrix is called the GEIS, a isis called of the focus S w.r.t, the directrix and also upon the value of | 5. Apoint of intersection of a conic with its axis 1s ca the eccentricity ¢. Two different cases arise, - | a vertex. Case (1): When the focus lies on the directrix: In this case A D=abe + Ugh — af?— bg*— ch*=0 and the general equation General Equation of a Conic: of a conic represents a pair of straight lines and if: | e >| the lines will be real and distinct intersecting at S, g) and direc- e= 1 the lines will be coincident, } The general equation of a conic with focus (P, li ease itt my + n= 0 is e <1 the lines will be imaginary, 
