Math topic中文

Equation straight line

interpreting and finding the equation of a straight line graph in the form y=mx+cy = mx + c

Practice questions

  1. 1The sketch shows the graph of y=kxay = kx^a. The points A(-2, -0.75) and B(0, -3) lie on the graph. Find the values of kk…
  2. 2过双曲线CC：x2a2−y2b2=1(a>0,b>0) \dfrac {x^{2}}{a^{2}}- \dfrac {y^{2}}{b^{2}} =1(a > 0 , b > 0)的左焦点FF且斜率为12 \dfrac {1}{2}的直线ll与双曲线…
  3. 3Solutions to this question by accurate drawing will not be accepted. The diagram below shows a triangle ABC, with A(3,6)A(3,6)…
  4. 4若直线{x=1−ty=2+3t(t\begin{cases}{x=1-t}\\ {y=2+3t}\end{cases}(t为参数))与直线y=kx−1y=kx-1平行，则常数k=()k=(\quad) A. −3-3 B. −13-\dfrac{1}{3}…
  5. 5已知圆心为CC的圆过点A(0,−6)A(0,-6)和B(1,−5)B(1,-5)，且圆心在直线ll：x−y+1=0x-y+1=0上． (1)求圆心为CC的圆的标准方程； (2)过点M(2,8)M(2,8)作圆的切线，求切线方程．
  6. 6曲线y=3x−2y=\sqrt{3x-2}在点(1,f(1))(1,f(1))处的切线方程为 A. x−2y+1=0x-2y+1=0 B. 3x−y−2=03x-y-2=0 C. 3x−2y−1=03x-2y-1=0 D. 3x+2y−5=03x+2y-5=0
  7. 7若曲线y=x−12y=x^{\mathrm{{-}}\frac{1}{2}}在点(a,a−12)(a,a^{\mathrm{{-}}\frac{1}{2}})处的切线与两个坐标轴围成的三角形的面积为1818，则aa的值为___.
  8. 8Complete the table of values for y=x−4x2y = x - \frac{4}{x^2}. Values are given to one decimal place where appropriate. Compl…
  9. 9The diagram shows a circle C1C_1 with centre P(5,3)P(5, 3). The circle touches the x-axis, the tangent OQ and another line Q…
  10. 10已知圆CC：(x+1)2+(y−1)2=1(x+1)^{2}+(y-1)^{2}=1与xx轴切于AA点，与yy轴切于BB点，设劣弧A^B \hat AB的中点为MM，则过点MM的圆CC的切线方程是()() A…
  11. 11The variables x and y are connected by the equation y=x+5x2−3y = x + \frac{5}{x^2} - 3 Some corresponding values of x and y are…
  12. 12The variables x and y are connected by the equation y=x35−2x+1y = \frac{x^3}{5} - 2x + 1. Some corresponding values of x and y a…
  13. 13已知过点P(1,32)P(1,\dfrac{3}{2})的曲线CC的方程为(x−1)2+y2+(x+1)2+y2=2a.(Ⅰ)\sqrt{{{(x-1)}^{2}}+{{y}^{2}}}+\sqrt{{{(x+1)}^{2}}+{{y}^{2}}}=2a.(Ⅰ)求曲线CC的标准…
  14. 14Complete the table of values for y=2x+20x−15y = 2x + \dfrac{20}{x} - 15. | x | 1 | 2.5 | 5 | 10 | 12.5 | 15 | 20 | |---|---|---|-…
  15. 15已知三个点A(0,0)A(0,0)，B(2,0)B(2,0)，C(4,2)C(4,2)，则△ABC\triangle ABC的外心的纵坐标是()(\quad) A. 32\dfrac{3}{2} B. 33 C. 52\dfrac{5}{2}…
  16. 16In the diagram, the points P, Q and R have coordinates (9, -3), (6,1) and (18, -3) respectively. Find the length of PQ.…
  17. 17下列各点中，在过点(−2,2)(-2 , 2)和(−2,4)(-2 , 4)的直线上的是(    )(\:\:\:\:) A. (−2,0)(-2 , 0) B. (−3,−3)(-3 , -3) C. (3,2)(3 , 2) D. (5,4)(5 , 4)
  18. 18ABCD is a parallelogram. A is the point (−6,−2)(-6,-2) and B is the point (−4,−7)(-4,-7). BC→=(8−2)\overrightarrow{BC} = \begin{pmatrix}8\\-2\end{pmatrix}…
  19. 19直线x+3y−1=0x+ \sqrt {3}y-1=0的斜率为()() A. 33 \dfrac { \sqrt {3}}{3} B. 3 \sqrt {3} C. −33- \dfrac { \sqrt {3}}{3} D. −3- \sqrt {3}…
  20. 20y=x34−2x+3y = \dfrac{x^3}{4} - 2x + 3. Complete the table of values for y=x34−2x+3y = \dfrac{x^3}{4} - 2x + 3. On the grid opposite, dra…
  21. 21过三点A(0,0)A(0,0)，B(0,2)B(0,2)，C(2,0)C(2,0)的圆MM与直线ll：kx−y+2−2k=0kx-y+2-2k=0的位置关系是()(\quad) A. 相交 B. 相切 C. 相交或相切 D. 相切或相离
  22. 22直线3x−y−3=0\sqrt{3}x{-}y{-}3{=}0的倾斜角为()({ }) A. 30∘30^{{∘}} B. 60∘60^{{∘}} C.  120∘\ 120^{{∘}} D.  150∘\ 150^{{∘}}
  23. 23The table below is for the function y=x34−2x+1y = \dfrac{x^{3}}{4} - 2x + 1. Complete the table of values for y=x34−2x+1y = \dfrac{x^{3}}{4} - 2x + 1…
  24. 24A is the point (2,3) and B is the point (3,-5). Find the equation of the line AB. Answer ... Find the length of AB. Answ…
  25. 25The equation of the line l1l_1 is x+4y=20x + 4y = 20. The line cuts the x-axis at point A and the y-axis at point B. Another…
  26. 26若曲线y=e−xy=e^{-x}上点PP处的切线平行于直线2x+y+1=02x+y+1=0，则点PP的坐标为 ___ ．
  27. 27Complete the table of values for y=2x2−2x.Valuesaregiventoonedecimalplacewhereappropriate.Onthegridopposite,drawthegraphofy=\dfrac{2}{x^{2}}-2x. Values are given to one decimal place where appropriate. On the grid opposite, draw the graph of …
  28. 28把下列参数方程化为普通方程，并说明它们各表示什么曲线： (1){x=5cos⁡φ,y=4sin⁡φ(φ(1)\begin{cases} x=5\cos φ, \\ y=4\sin φ \end{cases}(φ为参数))； (2){x=1−3t,y=4t(t(2)\begin{cases} x=1-3t, \\ y=4t \end{cases}(t…
  29. 29已知直线x−2y−2k=0x-2y-2k=0与两坐标轴围成的三角形面积不大于11，则实数kk的取值范围是___.
  30. 30求出满足下列条件的直线方程. (1)经过点A(−3,2)A(-3,2)且与直线x+3y−4=0x+3y-4=0垂直； (2)经过点B(2,7)B(2,7)且与直线2x−y−4=02x-y-4=0平行.
  31. 31点A(3,1)A(3,1)关于点M(4,−3)M(4,-3)的对称点是BB，直线ll过原点且过BB点， 则直线 ll 方程为 ；
  32. 32直线ax+by-2=0，若a，b满足2a+b=1，则直线必过定点 ．
  33. 33圆x2+y2−2x−5=0x^{2}+y^{2}-2x-5=0和圆x2+y2+2x−4y−4=0x^{2}+y^{2}+2x-4y-4=0的交点为AA、BB，则线段ABAB的垂直平分线方程为()(\quad) A. x+y−1=0                           x+y-1=0\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: …
  34. 34已知圆CC的圆心在直线y=x+1y=x+1上，且圆CC与xx轴相切，点P(−5,−2)P(-5,-2)在圆CC上，点Q(−4,−5)Q(-4,-5)在圆CC外． (1)求圆CC的方程； (2)若过点(−2,−4)(-2,-4)的…
  35. 35FF为抛物线CC：y2=4xy^{2}=4x的焦点，点M(m,4)M(m,4)在CC上，直线MFMF交CC的准线于点NN，则∣FN∣=()|FN|=(\quad) A. 54\dfrac{5}{4} B. 103\dfrac{10}{3}…
  36. 36Sketch the graph of y=2ln⁡xy = 2\ln x. In order to solve the equation xe2x=13xx e^{2x} = \dfrac{1}{3x}, a suitable straight line ha…
  37. 37直线ll：mx+y−m−2=0mx+y-m-2=0与圆CC：(x−3)2+(y−4)2=25(x-3)^{2}+(y-4)^{2}=25交于AA，BB两点，CC为圆心，当∠ACB∠ACB最小时，直线ll的方程是 ___ ．
  38. 38已知直线ll：3x+3y−1=03x+\sqrt{3}y-1=0，关于直线ll的以下四个结论： ①直线ll的倾斜角为2π3\dfrac{2\pi}{3}；②直线ll经过点(23,3)\left(\dfrac{2}{3},\sqrt{3}\right)…
  39. 39已知圆OO：x2+y2=4x^{2}+y^{2}=4和圆CC：(x−2)2+(y−3)2=1.(x-2)^{2}+(y-3)^{2}=1.现给出如下结论，其中正确的是()(\quad) A. 圆OO与圆CC有四条公切线 B. 过CC且在…
  40. 40设函数f(x)=ax+bxf(x)=ax+ \dfrac {b}{x}，曲线y=f(x)y=f(x)在点M(3,f(3))M( \sqrt {3},f( \sqrt {3}))处的切线方程为2x−3y+23=02x-3y+2 \sqrt {3}=0． ((Ⅰ))求f(x)f(x)…
  41. 41Given that the coordinates of point A is (−2,11)(-2,11) and point B is (5,−11)(5,-11). Find length ABAB. Answer ... equation of th…
  42. 42The variables x and y are connected by the equation y=13x(11−x2).Somecorrespondingvaluesofxandy,correctto1decimalplaces,aregiveninthefollowingtable.Calculatethevalueofp.Answerp=...Onthegridopposite,drawthegraphofy = \frac{1}{3}x(11 - x^2). Some corresponding values of x and y, correct to 1 decimal places, are given in the following table. Calculate the value of p. Answer p = ... On the grid opposite, draw the graph of …
  43. 43The points A(0,2) and B(1,0) lie on the graph y=x2+ax+by = x^2 + ax + b. Find the values of a and b. Answer a = ... b = ... C i…
  44. 44The diagram shows three points A(-16, 0), B(0, 12) and C(8, 2). A circle is drawn with centre C such that AB is a tangen…
  45. 45The position vector of A is (34)\begin{pmatrix}3\\4\end{pmatrix} and the position vector of B is (710)\begin{pmatrix}7\\10\end{pmatrix}…
  46. 46Let y=2x3−x2−10xy = 2x^3 - x^2 - 10x. Complete the table of values for y=2x3−x2−10xy = 2x^3 - x^2 - 10x. On the grid opposite, draw the grap…
  47. 47设函数f(x)=xln⁡ x+2x3f(x)=x\ln\:x+2x^{3}，则曲线y=f(x)y=f(x)在点(1,2)(1,2)处的切线方程是___.
  48. 48已知椭圆C:x2a2+y2b2=1(a>b>0)\text{C}:\dfrac{{{x}^{2}}}{{{a}^{2}}}+\dfrac{{{y}^{2}}}{{{b}^{2}}}=1(a>b>0)的右焦点为F(1,0)F(1,0)，过原点OO的动直线与椭圆CC交…
  49. 49The diagram shows two congruent isosceles triangles, PQS and RSQ. PQ and RS are parallel to the x-axis. Write down the c…
  50. 50直线2x+4y−3=02x+4y-3=0的斜率为___.
  51. 51求过点 (1,2)(1, 2) 且斜率为 −3-3 的直线方程。
  52. 52The diagram shows a trapezium in which ADAD is parallel to BCBC and angle ADC=ADC = angle BCD=90∘BCD = 90^\circ. The points BB…
  53. 53The variables x and y are connected by the equation y=2x+6x−7y = 2x + \dfrac{6}{x} - 7. Some corresponding values of x and y ar…
  54. 54若点P(1,1)P(1,1)为圆x2+y2−6x=0x^{2}+y^{2}-6x=0的弦MNMN的中点，则弦MNMN所在直线的方程为 ()(\quad) A. 2x+y−3=02x+y-3=0 B. x−2y+1=0x-2y+1=0 C. x+2y−3=0x+2y-3=0…
  55. 55P is the point (3, −1) and Q is the point (−5, 5). Find ∣PQ∣|PQ|. Answer ∣PQ∣|PQ| = ... units The line PQ intersects the x-a…
  56. 56若点A（1，1）、B（2，0）在直线1：y=kx的两侧，则实数k取值范围为___．
  57. 57The variables x and y are connected by the equation y=32x+5x−7y = \frac{3}{2}x + \frac{5}{x} - 7. Some corresponding values of x…
  58. 58A is the point (1,−4)(1, -4) and B is the point (−7,−2).(-7, -2). The point C is the result of the translation of point B by the c…
  59. 59Leanne says that the equation of the line AB is 2y=−4x+12y = -4x + 1 and the equation of the line PQ is 4y=−9x+24y = -9x + 2. Is she…
  60. 60In the diagram, A is the point (−2,4)(-2, 4), and C is the point (4,7)(4, 7). AB is a vertical line. The line BC has gradient 32\frac{3}{2}…