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直线与圆的基础知识是解析几何部分的基石,是解决很多数学问题行之有效的途径.将这部分知识学活、学实十分必要,现举若干典型问题加以剖析,以期对大家有所帮助. 例1已知直线l的倾斜角为α,且-1≤tanα≤1,则α的范围____. 解:因为-1≤tanα≤1,所以又0≤α<π,因此,3/4π≤α<π或0≤α≤π/4. 文华点精:由倾斜角的范围确定出分界线0,是本题的关键,也是容易出错的地方. 例1直线(a+2)x+(1-a)y-3=0与(a-1)x+(2a+3)y+2=0 互相垂直,则a的值为____. 解:A1=a+2,A2=a-1,B1=1-a,B2=2a+3.因为两直线垂直,所以(a+2)(a-1)+(1-a)(2a+3)=0,整理得a=±1. 文华点精:此题极易漏解,需分a=1,a≠1两种情况讨论.其实本题
The basic knowledge of the straight line and the circle is the cornerstone of the analytical geometry. It is an effective way to solve many problems of mathematics. It is necessary to learn and study this part of knowledge. Now we will analyze some typical problems to help everyone. In Example 1, it is known that the inclination angle of the straight line l is α, and -1≤tanα≤1, the range of α is ____. Solution: Because -1≤tanα≤1, so 0≤α<π, therefore, 3/ 4π ≤ α <π or 0 ≤ α ≤ π / 4. Wenhua point fine: From the range of tilt angle to determine the demarcation line 0, is the key to this problem, but also error-prone. Example 1 Line (a + 2) x + (1-a) y-3=0 and (a-1)x+(2a+3)y+2=0 are perpendicular to each other, then the value of a is ____. Solution: A1=a+2, A2=a- 1, B1 = 1 - a, B2 = 2a + 3. Because the two straight lines, so (a + 2) (a-1) + (1-a) (2a + 3) = 0, finishing a = ± 1 Wenhua point fine: This question is easily misunderstood, need to divide a=1, a≠1 two situations discussion. Actually this question