Math topic中文

Gradient two points

finding the gradient of a straight line given the coordinates of two points on it

Practice questions

1已知圆 $C$ ： $(x+1)^{2}+(y-1)^{2}=1$ 与 $x$ 轴切于 $A$ 点，与 $y$ 轴切于 $B$ 点，设劣弧 $\hat AB$ 的中点为 $M$ ，则过点 $M$ 的圆 $C$ 的切线方程是 $()$ A…
2已知过点 $P(1,\dfrac{3}{2})$ 的曲线 $C$ 的方程为 $\sqrt{{{(x-1)}^{2}}+{{y}^{2}}}+\sqrt{{{(x+1)}^{2}}+{{y}^{2}}}=2a.(Ⅰ)$ 求曲线 $C$ 的标准…
3ABCD is a parallelogram. A is the point $(-6,-2)$ and B is the point $(-4,-7)$ . $\overrightarrow{BC} = \begin{pmatrix}8\\-2\end{pmatrix}$ …
4圆 $x^{2}+y^{2}-2x-5=0$ 和圆 $x^{2}+y^{2}+2x-4y-4=0$ 的交点为 $A$ 、 $B$ ，则线段 $AB$ 的垂直平分线方程为 $(\quad)$ A. $x+y-1=0\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:$ …
5Given that the coordinates of point A is $(-2,11)$ and point B is $(5,-11)$ . Find length $AB$ . Answer ... equation of th…
6K is the point $(7, -8)$ and L is the point $(x, y).\n\nThe gradient of the line KL is$ \frac{2}{3} $.\n\nMaverick claims that it is possible to express$ …
7The points A(0,2) and B(1,0) lie on the graph $y = x^2 + ax + b$ . Find the values of a and b. Answer a = ... b = ... C i…
8The 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…
9The triangle with vertices A (2, 5), B (−2, −3) and C (2, −2) is shown in the diagram below. Find (a) the area of triang…
10The diagram shows two congruent isosceles triangles, PQS and RSQ. PQ and RS are parallel to the x-axis. Write down the c…
11The diagram shows a trapezium in which $AD$ is parallel to $BC$ and angle $ADC =$ angle $BCD = 90^\circ$ . The points $B$ …
12The variables x and y are connected by the equation $y = 2x + \dfrac{6}{x} - 7$ . Some corresponding values of x and y ar…
13若点 $P(1,1)$ 为圆 $x^{2}+y^{2}-6x=0$ 的弦 $MN$ 的中点，则弦 $MN$ 所在直线的方程为 $(\quad)$ A. $2x+y-3=0$ B. $x-2y+1=0$ C. $x+2y-3=0$ …
14若双曲线的中心为原点， $F(0,-2)$ 是双曲线的焦点，过 $F$ 的直线 $l$ 与双曲线相交于 $M$ ， $N$ 两点，且 $MN$ 的中点为 $P(3,1)$ ，则双曲线的方程为 $(\quad)$ A. $\dfrac{x^{2}}{3}-y^{2}=1$ …
15In the diagram, A is the point $(-2, 4)$ , and C is the point $(4, 7)$ . AB is a vertical line. The line BC has gradient $\frac{3}{2}$ …
16若 $A(\text{-}2\text{,}3)$ ， $B(3\text{,-}2)$ ， $C(1\text{,}m)$ 三点共线，则 $m$ 的值为 $()$ A. $\text{-}2$ B. $\text{-}1$ C.…
17Triangle ABC is equilateral. CAD and ABE are straight lines and AD = BE. Show that triangle ABD and triangle BCE are con…
18The point A is (0,7) and the point B is (6,9). Express $\overrightarrow{AB}$ as a column vector. The equation of AB is x…
19已知椭圆 $C： \dfrac {x^{2}}{3}+ \dfrac {y^{2}}{2}=1$ 上的动点 $P$ 与其顶点 $A(- \sqrt {3},0)$ ， $B( \sqrt {3},0)$ 不重合． $($ Ⅰ $)$ 求证…
20The coordinates of P and Q are (0, 3) and (15, 12) respectively. Find the equation of PQ. Find the perimeter of trapeziu…
21已知椭圆 $\dfrac{x^{2}}{3}+\dfrac{y^{2}}{4}=1$ 的弦被点 $(1,1)$ 平分，那么这条弦所在的直线方程为 $(\quad)$ A. $4x+3y-7=0$ B. $4x-3y-7=0$ C.…
22Points P, Q and R have coordinates $(1, 1)$ , $(5, 11)$ and $(9, 1)$ respectively. M is the midpoint of QR. Find the coor…
23已知过两点 $A(-3,m)$ ， $B(m,5)$ 的直线与直线 $3x+y-1=0$ 平行，则 $m$ 的值是 $()$ A. $3$ B. $7$ C. $-7$ D. $-9$
24设双曲线 $\dfrac {x^{2}}{a^{2}}- \dfrac {y^{2}}{b^{2}}=1(a > 0,b > 0)$ 的左、右顶点分别为 $A$ 、 $B$ ，点 $P$ 在双曲线上且异于 $A$ 、 $B$ 两点， $O$ …
25The gradient of the line joining the points $(-3+2a, 7)$ and $(a+1, 2)$ is $-\frac{2}{3}$ . Find the value of a. Answer a…
26ABCD is a parallelogram. Point A lies on the y-axis and coordinates of D is (6, -1). AC is a horizontal line and gradien…
27Line l passes through the points (-4, 4) and (8, -2). Find the equation of line l. Answer ... The equation of line m is…
28The diagram shows a square ABCD. The diagonals of the square intersect at W and X is a point on the diagonal BD. Y lies…
29已知椭圆 $C： \dfrac {x^{2}}{a^{2}}+ \dfrac {y^{2}}{b^{2}}=1(a > b > 0)$ 的左焦点 $F(-2,0)$ 左顶点 $A_{1}(-4,0)$ ． $($ Ⅰ $)$ 求椭圆 $C$ …
30The diagram shows the curve y = x^2 + px + q. The points A(0, −5) and B(2, −9) lie on the graph. B(2, −9) is the minimum…