(1)
Find the centre, vertex, axis of symmetry, transverse semi-axis, conjugate semi-axis, eccentricity, focus, directrix, length of latus rectum and asymptotes for the following hyperbola and sketch the graph.
求下列各双曲线的中心, 顶点, 对称轴, 半实轴长, 半虚轴长, 离心率, 焦点, 准线, 通径长度和渐近线並描其图形.
(a) 9x – y
= 9
(b) y – 4x
= 1
(c) 4x – 9y
– 16x – 18y – 29 = 0
Answer (a) :
Answer (b) :
Answer (c) :
Find the equation of the hyperbola with center at (-7, -2), transverse axis parallel to the x-axis, eccentricity , latus rectum
.
求中心为(-7, -2), 实轴平行于x轴, 离心率为 及通径长度为
的双曲线方程式.
Answer :
![Rendered by QuickLaTeX.com (x + 7)^2 - 9(y + 2)^2 = 36](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-54fd7c01c4ec668d739bb9a58d89a31a_l3.png)
Find the equation of the hyperbola with asymptotes 2x – y = 0, 2x + y – 4 = 0 and passes through the point (6, 10).
求其渐近线为2x – y = 0, 2x + y – 4 = 0且经过点 (6, 10) 的双曲线方程式.
Answer :
Find the equation of the hyperbolic with center (3, -6), conjugate axis parallel to the x-axis, distance between foci , distance between directrices
.
求中心为(3, -6), 虚轴平行于x轴, 焦点之距离为 且准线的距离是
的双曲线方程式
Answer :
![Rendered by QuickLaTeX.com (y + 6)^2 - 4(x - 3)^2 = 36](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-8400961e050057ee6bd29248bd70d87c_l3.png)
Given that P is on the right side of the hyperbola, its distance to the right directrix is
, calculate the distance of P to the left focus.
己知双曲线 右支上一点P到右准线的距离为
,求P点到左焦点的距离。
Answer :
![Rendered by QuickLaTeX.com \frac{1}{3}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-e63e48332471cc9171675f2cb9c542fd_l3.png)
If the hyperbola and circle
don’t have intersection point, find the range of the real value k.
若双曲线 与圆
沒有公共点, 求实数 k 的取值范围.
Answer :
![Rendered by QuickLaTeX.com k > \frac{1}{3}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-9d859d5d291392f1d04c60001f0a50a0_l3.png)
![Rendered by QuickLaTeX.com k < -\frac{1}{3}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-437898cbe40dec7b0f2489465c87e318_l3.png)