Recall from geometry that the line draw tangent to a circle
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Recall from geometry that the line draw tangent to a circle is perpendicular to the radius line drawn to the point of tangency.Use this fact to find the equation of the line tangent to the circle x^2 + y^2 = 25 at (-3,4).
英语水平有限,能看得懂意思,但是要解释的话我还是用中文吧,仅供楼主参考.
与圆相切于(-3,4),所以圆心到(-3,4)的这条线必定与该直线垂直
过圆心(0,0)与(-3,4)的直线为:
y=-4x/3
所以该直线的斜率为3/4
y=3x/4+b,(-3,4)
>
4=-9/4+b
>b=25/4
>
y=3x/4+25/4
>3x-4y = -25
与圆相切于(-3,4),所以圆心到(-3,4)的这条线必定与该直线垂直
过圆心(0,0)与(-3,4)的直线为:
y=-4x/3
所以该直线的斜率为3/4
y=3x/4+b,(-3,4)
>
4=-9/4+b
>b=25/4
>
y=3x/4+25/4
>3x-4y = -25
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