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).

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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

Chords of the circle p=29cosθ which pass through the pole are extended a distance 2b. Find the locus of their extremities.

关于直交轴有三直线: x=0,y=0,x/a+y/b=1.求与此三直线相切之圆之方程式.

求二直线y=m1x+c1,y=m2x+c2及y轴所包围之三角形之面积.

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.

在平地上一点 A，测得某山顶 P 之仰角 (elevation) 为 60°，自 A 点，在平地上，向山麓前进 800 尺至 B 点.自 B 点沿一与平地倾斜 30°之斜坡，再向山顶前进 800 尺，至 C 点，在 C 点测得山顶 P之仰角为 75°.若 A,B,C,P四点在一垂直平面内，求此山之高.

于 A,B,C 三阵地测得敌机之仰角为 60°,45°,45°，今 B 地在 A 地正北 3000尺，C 地在 A 地之正西 4000 尺，求敌机之高，并讨论之.

证明自椭圆二焦点至其任意切线之垂直距离，其乘积为一常数.

试求椭圆中诸平行弦之中点轨迹的方程式.

直线与方程

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.

过点(1,2)且与直线2x + y - 1 = 0平行的直线方程是__________.

如果AC < 0，且BC < 0，那么直线Ax + By + C = 0不通过【】

点(4,0)关于直线5x+4y+21=0的对称点是【】

已知直线l1和l2夹角的平分线为y=x,如果l1的方程是ax+by+c=0(ab>0),那么l2的方程是【】

直线bx+ay=ab(a<0,b<0)的倾斜角是【】