About Lesson
5.2 Parabola 抛物线
1. Find the vertex, focus, directrix of the following parabola and sketch the graph.
试求以下方程式之顶点, 焦点, 准线並描其图形.
(a)
(b)
(c)
(d)
Answer 1(a) :
Answer 1(b) :
Answer 1(c) :
Answer 1(d) :
2. Find the equation of the parabola with vertex at (5, -2) and focus at (5, -4)
求顶点为(5, -2)及焦点为(5, -4)的抛物线方程式
Answer:
![Rendered by QuickLaTeX.com x^2 - 10x + 8y + 41 = 0](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-5b52482b7c5bc6d279fb3cc86d2b0aca_l3.png)
3. A parabola has its axis parallel to the y-axis, one end of its latus rectum is at (9, 6) and the vertex is at (5, 4). Find
一抛物线其对称轴平行于y轴, 通径的一端在(9, 6)且顶点在(5, 4). 求
(a) the length of the latus rectum
其通径长度
(b) the equation of the parabola
该抛物线的方程式
Answer :
(a) 8
(b) x– 10x – 8y + 57 = 0
4. Find the equation of a parabola where the vertex of the parabola is (-2, 3), the focus is on the line 4x – 3y + 5 = 0 and the symmetric axis is parallel to
求一拋物线方程式其中该拋物线的顶点坐标是(-2, 3),焦点在直线4x – 3y + 5 = 0上且对称轴平行于
(a) x – axis,
x-轴
(b) y – axis
y-坐标轴,
Answer:
(a)
![Rendered by QuickLaTeX.com (y - 3)^2 = 12(x + 2)](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-688c3fd951210778c9f79266485db6ba_l3.png)
(b)
5. Find the equation of a parabola with vertex on the line y = 2x, symmetric axis parallel to the x-axis and passing through (1½, 1 ) and (3, 4)
求一抛物线的方程式其顶点在直线y = 2x上, 对称轴平行于x轴且经过点 (1½, 1) 及 (3, 4).
Answer:
![Rendered by QuickLaTeX.com (y - 2)^2 = 2(x - 1)](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-e211070541bf9e75794e614669319d3d_l3.png)
![Rendered by QuickLaTeX.com (y - 7)^2 = -8(x - \frac{7}{2} )](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-ee636dc9cae7dcd5010f18ff18e17802_l3.png)
6. Find the equation of a parabola through (-1, -3) and (2, 1.5), whose axis is parallel to the y-axis and latus rectum equal to 6.
求经过 (-1, -3) 和 (2, 1.5), 其对称轴平行于y轴及通径长等于6的抛物线方程式.
Answer:
![Rendered by QuickLaTeX.com (x - 5)^2 = -6(y - 3)](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-2faaa5bce9bf4e3b61db260f0293c76e_l3.png)
![Rendered by QuickLaTeX.com (x + 4)^2 = 6(y + \frac{9}{2})](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-f4b5bb257c7b677b14a522ceecf6b60a_l3.png)
7. A parabola has directrix x = 6, axis y = -5 and latus rectum equal to 9. Find its equation.
一抛物线其准线为x = 6, 对称为y = -5 和通线长等于9, 求其方程式.
Answer:
![Rendered by QuickLaTeX.com (y + 5)^2 = -9(x - 3\frac{3}{4})](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-026a69af2c7fa8b722264a18aeecdd50_l3.png)
![Rendered by QuickLaTeX.com (y + 5)^2 = 9(x - 8\frac{1}{4})](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-1149f30ed6d38056139777aa5fd23955_l3.png)