3. Conic Sections Contents Memorial University （3所示。）.pdfVIP

ENGI 3425 3. Conic Sections 0 1 3. Conic Sections Contents: 3.1 Standard Form 3.2 General Conic Sections 3.3 Polar Form for Conic Sections 3.1 Standard Form All members of the family of curves known as conic sections can be generated, (as the name implies), from the intersections of a plane and a double cone. The Cartesian equation of any conic section is a second order polynomial in x and y . The only cases that we shall consider in this section are such that any axis of symmetry is parallel to a coordinate axis. For all such cases, the Cartesian equation is of the form Ax 2 Cy 2 Dx Ey F 0 where A , C, D, E and F are constants. There is no “xy” term, so B = 0. The slope of the intersecting plane is related to the eccentricity, e of the conic section. Circle 2 2 2 x y r or, if the centre is at h, k  , x h 2  y k 2 r 2     A parametric form for a circle, centre at the origin, radius r is x, y r cos, r sin , 0   2 .       ENGI 3425 3.1 – Standard Form 02 Ellipse Cartesian equation: 2 2 x y  1 a2 b2 where b2 a2 1 e2  The circle is clearly a special case of