以双曲线29-&y216＝1的右焦点为圆心，且与其渐近线相切的圆的方程是（　　）A. x2+y2-10x+9=0B. x2+y2-10x+16=0C. x2+y2+10x+16=0D. x2+y2+20x+9=0
乱颜是神已絓
右焦点即圆心为（5，0），一渐近线方程为，即4x-3y=0，，圆方程为（x-5）2+y2=16，即x2+y2-10x+9=0，故选A．
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其他类似问题
求出双曲线29-&y216＝1的右焦点得到圆心，在求出圆心到其渐近线的距离得到圆的半径，从而得到圆的方程．
本题考点：
双曲线的简单性质．
考点点评：
本题考查双曲线的焦点坐标和其渐近线方程以及圆的基础知识，在解题过程要注意相关知识的灵活运用．
求右焦点到渐近线的距离，用点到线距离公式。求得的距离即为半径，再把圆心坐标和半径带入标准圆方程。就求到了！
右焦点为(5,0)渐近线的方程为4x±3y=0圆心(5,0)到4x±3y=0的距离为4，所以圆的方程为(x-5)^2+y^2=16.
大学生不能帮助你了
c=√（9+16）=5∴右焦点坐标为（5,0）渐近线方程为：y=±4x/3，即：±4x-3y=0则右焦点到渐近线的距离d=|±4*5-3*0|/√（16+9）=4∴圆的方程为：（x-5）²+y²=16
同意高中数学达人小赵。
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