高中数学-高考试题(解析几何 1947年直线与方程)

问答题（1947年解析几何）

Find the distance from the point (-1, -4) to the straight line which is drawn through (-2,6) and the perpendicular to the line joining (3,6) and (-5,-1).

答案解析

暂无答案

讨论

高中数学

Two towers, A and B, on the shore of a lake can be observed from only one point C on the opposite shore. The lines joining the bases of two towers subtend anangle of 63°42' at C. The heights of the towers are 132 feet and 89 feet, and the angle of elevation of the tops as seen from C are 8°13' and 7°21' respectively.Find the distance AB.

The sides of a triangle are 149,163 and 222. To find(1) The area of the triangle.(2) The radius of the inscribed circle.(3) The angles of the triangle.

A tower of 20.7 feet high stands at the edge of the water on a bank of a river. From a point directly opposite to the tower on the other side of the river above the water, the angle of elevation of the top of the tower is 27°17' and the angle of depression of the image of its top in the water is 38°12'. Find the width of the river.

The base of a right circular cone has a diameter of 25 feet and its slant height is 40 feet. The surface of the cone is cut along a straight line from its vertex to a point on the base, and the surface is then spread out flat to form a sector of a circle. Find the angle of its sector in degrees.

Solve secx - cotx = cscx - tanx

Solve 1+1+2/(1-tan²⁡x )-(3-tan²⁡x)/(1-3 tan²⁡x )=0

Prove that：tan-1⁡1/3+tan-1⁡1/5+tan-1⁡1/7+tan-1⁡1/8=45°

Prove that：(sin75°+sin15°)/(sin75°-sin15°)=tan60°

Given ∠1=∠2,a,b,c，find d.

Transform the difference of two squares into a rectangle, the ratio of two sides being 2 : 3.

平面解析几何

已知λ>0，向量|a|=|b|=|c|=λ，且a∙b=0,c∙b=1,c∙a=2，则λ=________.

已知长方形的四个顶点A(0,0),B(2,0),C(2,1)和D(0,1).一质点从AB的中点P_0沿与AB夹角为θ的方向射到BC上的点P1后，依次反射到CD,DA和AB上的点P2,P3和P4(入射角等于反射角).设P4的坐标为(x4,0).若1<x4<2，则tanθ的取值范围是【】

在某海滨城市附近海面有一台风，据监测，当前台风中心位于城市O(如图)的东偏南θ(θ=arccos⁡(√2/10))方向300km的海面P处，并以20km/h的速度向西偏北45°方向移动.台风侵袭的范围为圆形区域，当前半径为60km，并以10km/h的速度不断增大.问几小时后该城市开始受到台风的侵袭?

在∆ABC中，(CA)→=a,(CB)→=b,D是AC的中点,(CB)→=2(BE)→,试用a,b表示(DE)→=________；若(AB)→⊥DE→，求∠C的最大值为______.

在∆ABC中，a=√6,b=2c,cosC=-1/4.(1)求∠C的大小；(2)求sinB的值；(3)求sin⁡(2A-B)的值.

A boy standing cft. behind and opposite the middle of a foothall goal sees that the angle of elevation of the nearer is A and the angle of elevation of the farther one is B. Show that the length of the field is c(tanAcotB-1).

有ABC三角形，已知B=15°,b=√3-1,c=√3+1，试求其余各项.

于正东正南甲乙二地，测得某山之仰角为 45°及 30°，今甲乙两地之距离为2400 尺，求山高.

求圆x²+y²=17之切线，使平行于直线x+4y=5.

A,B,C 为共线之三定点，动点 P 至A，B与 B，C 所张之角恒相等，试求 P 点之轨迹.

直线与方程

已知一圆及一直线，求作该圆之切线，使其自切点至该直线间之线段，等于已知长.

设有一三角形ABC：假定A及B两顶为固定不移，其他一C在AC²+BC²=2/5 AB²之条件下运动，则其轨迹为何如？

求已知圆 x²+y² - 6x +4y = 12 之两切方程式，与一已知线 4x + 3y +5=0平行.

点 (0, −1) 到直线 y = k(x + 1) 距离的最大值为【】

若直线 l 与曲线 y = 和圆 x2 + y2 = 1/5 相切, 则 l 的方程为【】

用解析几何方法证明三角形的三条高线交于一点.

已知两点P(-2,2),Q(2,2)以及一条直线l:y=x.设长为的线段AB在直线l上移动.求直线PA和QB的交点M的轨迹方程.(要求把结果写成普通方程)

自点A(-3,3)发出的光线l射到x轴上，被x轴反射，其反射光线所在直线与圆x2+y2-4x-4y+7=0相切，求光线l所在直线的方程.

如图，若图中的直线l1,l2,l3的斜率分别为k1,k2,k3，则【】

已知l1,l2是过点P(-,0)的两条互相垂直的直线，且l1,l2于双曲线y2 - x2=1各有两个交点，分别为A1 B1 和A2 B2.(Ⅰ)求l1的斜率k的取值范围；(Ⅱ)若|A1 B1 |= |A2 B2 |,求l1,l2的方程.