14.1 Tangent and Normal 切线与法线

---

 

1.
Find the coordinate of the point on at which the curve has gradient 3. Hence find the equation of the tangent.

求在曲线上其斜率为3的点之坐标。据此求切线方程式。

2.
Find the equation of the normal to the curve at the point where the curve cuts the y-axis.

求曲线与 y轴 交点的法线方程式。

3.
P is the point (4, 7) on the curve . Find the slope of the curve at P, and the equation of the tangent at this point. The tangent at another point Q on the curve is perpendicular to the tangent at P. Calculate the x-coordinate of Q.

P 点 (4, 7) 在曲线 上. 求在 P的斜率, 和该点的切线方程式. 在曲线的另外一个点 Q 的切线与 P点的切线互相垂直. 计算Q 的 x坐标.

4.
Find the coordinates of the parabola at which
求在抛物线 上的点坐标使到

(a) the gradient is zero
其斜率是零，

(b) the tangent is parallel to y = 2x + 6
其切线方程式平行于y = 2x + 6，

(c) the tangent is perpendicular to 3x + 2y = 8 [
其切线垂直于3x + 2y = 8

5.
Given that the curve has a gradient of –5 at the point (2, –2),
已知曲线 在点 (2, –2) 的斜率是–5,

(a) find the value of a and b,
求a 和 b的值，

(b) the equation of normal at (2, –2).
在(2, –2)的法线方程式

6.
For the curve with equation calculates the possible values of k such that the tangents at the points with x coordinates 1 and respectively are perpendicular.

一曲线方程为 ，试计算所有的的 k 使得在 x 坐标为 1 和 的切线互相垂直。

7.
If the tangent and normal at (4, 8) to the curve meet the x-axis at T and G, prove that the length of TG is = 26.

若在曲线 的点(4, 8) 的切线和法线与 x-轴分别角于 T 和 G, 试证 TG 长是 26.