圆锥曲线小结summaryofconicsection.docxVIP

PAGE / NUMPAGES 圆锥曲线小结（Summary of Conic Section） 圆Circle 标准方程： 以为圆心，r为半径． 一般方程：，表示圆的前提条件是. 椭圆Ellipse An ellipse is the set of all points in the plane, the sum of whose distances from two fixed points, called foci, is constant．，离心率． 焦点位置由分母大小决定，在较大分母所对应的轴上． 双曲线Hyperbola A hyperbola is the set of all points in the plane in which the difference of the distances from two distinct fixed points, called foci, is constant． 离心率． 焦点位置由分母的正负决定，在正分母所对应的轴上． Standard Form of the Equation of a Hyperbola Orientation Description Asymptote 抛物线Parabola A parabola is defined as the set of all points in a plane that are the same distance from a given point, called the focus, and a given line, called the directrix. 离心率，焦点在一次项所对应的轴上． The general form of the equation of a parabola is, when the directrix is parallel to the y-axis, or , when the directrix is parallel to the x-axis. General Form Exercise Identify the conic section represented by each equation. Identify the center, vertices, and foci of the ellipse with equation .Then graph the equation. Identify the center, vertices, foci, and equations of the asymptotes of the graph of the hyperbola with equation. Then graph the equation. Identify the vertex, focus, and equations of the axis of symmetry and directrix for the parabola with equation . Then graph the equation. Write the equation of the ellipse that meets each set of conditions. The foci are at (2, 0) and, and a=7. The semi-major axis has length units, and the foci are at and. Write the equation of the hyperbola that meets each set of conditions. The center is at (4, 2), , and it has a vertical transverse axis. A vertex is at (4, 5), the center is at (4, 2), and an equation of one asymptote is. Write the equation of the parabola that meets each set of conditions. The vertex is at, and the focus is at (2, 1). The parabola passes through the point at (5, 2), has a vertical axis, and has a maximum at (4, 3).