共50条信息
已知圆\(C\)\({\,\!}_{1}\):\((\)\(x\)\(-2)^{2}+(\)\(y\)\(-3)^{2}=1\),圆\(C\)\({\,\!}_{2}\):\((\)\(x\)\(-3)^{2}+(\)\(y\)\(-4)^{2}=9\),\(M\),\(N\)分别是圆\(C\)\({\,\!}_{1}\),\(C\)\({\,\!}_{2}\)上的动点,\(P\)为\(x\)轴上的动点,则\(|\)\(PM\)\(|+|\)\(PN\)\(|\)的最小值为 .
双曲线\(\dfrac{{{x}^{2}}}{{{a}^{2}}}-\dfrac{{{y}^{2}}}{{{b}^{2}}}=1(a > 0,b > 0)\)上一点\(M(-3,4)\)关于一条渐近线的对称点恰为右焦点\(F_{2}\),则该双曲线的标准方程为________.
圆\(C_{1}\):\({\left(x-1\right)}^{2}+{\left(y-3\right)}^{2}=9 \)和\(C_{2}\):\({x}^{2}+{\left(y-2\right)}^{2}=1,M,N \)分别是圆\(C\)\(1\),\(C\)\(2\)上的点,\(P\)是直线\(y=-1 \)上的点,则\(\left|PM\right|+\left|PN\right| \)的最小值是
已知圆\(:\)关于直线对称,圆心在第四象限,半径为\( \sqrt{2} \).
\((1)\)求圆的方程\(;\)
\((2)\)是否存在直线\(l\)与圆\(C\)相切,且在\(x\)轴上的截距是\(y\)轴上的截距的\(2\)倍\(?\)若存在,求直线\(l\)的方程\(;\)若不存在,说明理由.
已知\(M\)是抛物线\({y}^{2}=2x \)上一点,\(N\)是圆\({x}^{2}+{\left(y-2\right)}^{2}=1 \)关于直线\(x-y=0 \)对称的曲线\(C\)上任意一点,则\(\left|MN\right| \)的最小值为__________.
圆\(C_{1}\):\((\)\(x\)\(-1)^{2}+(\)\(y\)\(-3)^{2}=9\)和\(C_{2}\):\(x\)\({\,\!}^{2}+(\)\(y\)\(-2)^{2}=1\),\(M\),\(N\)分别是圆\(C_{1}\),\(C_{2}\)上的点,\(P\)是直线\(y\)\(=-1\)上的点,则\(|PM|+|PN|\)的最小值是______
已知圆\(C_{1}:(x+6)^{2}+(y-5)^{2}=4\),圆\(C_{2}:(x-2)^{2}+(y-1)^{2}=1\),\(M\),\(N\)分别为圆\(C_{1}\)和\(C_{2}\)上的动点,\(P\)为\(x\)轴上的动点,则\(|PM|+|PN|\)的最小值为______.
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