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Conic Section 复习课
Conic Section Understand the geometric definitions of the conic section. Write the equations of the conic section in standard form. Distinguish between the equations of the circle , ellipse, and the hyperbola. Use the equations of the conic section to sketch the graphs and locate the foci and vertices Find the equations of the associated lines: asymptotes , directrix. For the equations of conic section in polynomial form ,state the transformations of the graph from the central form. Objectives of this chapter: What do the words “circle””ellipse”bring to your mind ? transformation Equation: Graph: Circle: x y O (a ,b) ellipse Geometric definition: An ellipse is the set of all points P(x ,y) in a plane the sum of whose distances from two fixed points , F1 and F2 , is constant. Equation: x y O Graph: Transformation: vertices: (h-a , k) (h+a , k) foci: (h-c , k) (h+c , k) ellipse graph equation foci vertices major axis minor axis centered at (0,0) ab (c, 0) (-c,0) (a, 0) (-a,0) Horizontal 2a Vertical 2b ab (0, c ) (0,-c) (0, a ) (0,-a) Vertical 2a Horizontal 2b centered at (h ,k) ab (h+c, k) (h-c , k) (h+a, k) (h-a , k) Horizontal 2a Vertical 2b Vertical 2a Horizontal 2b x y O x y O x y O x y O Summary: What could you recall about hyperbola and parabola? Hyperbola: A hyperbola is the set of all points(x , y) in a plane, the difference of whose distances from two distinct fixed points (foci) is a positive constant. Geometric meaning vertices: (a,0) ,(-a,0) foci: (c,0), (-c,0) equation transverse axis: 2a conjugate axis: 2b x y asymptotes transformation x y hyperbola graph equation foci vertices transverse axis asymptote centered at (0,0) (c, 0) (-c,0) (a, 0) (-a,0) Horizontal 2a (0, c ) (0,-c) (0, a ) (0,-a) Vertical 2a centered at (h ,k) (h+c, k) (h-c , k) (h+a, k) (h-
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