共50条信息
已知\(A(0,1)\),\(B(\sqrt{2},0)\),\(O\)为坐标原点,动点\(P\)满足\(|\overrightarrow{OP}|=2\),则\(|\overrightarrow{OA}+\overrightarrow{OB}+\overrightarrow{OP}|\)的最小值为
设函数\(f(x)={{(x-a)}^{2}}+{{(2\ln x-2a)}^{2}}\),其中\(x > 0,a\in {R}\),存在\({{x}_{0}}\)使得\(f({{x}_{0}})\leqslant \dfrac{4}{5}\)成立,则实数\(a\)的值是\((\) \()\)
设\(P,Q\)分别为\({{x}^{2}}+{{\left( y-6 \right)}^{2}}=2\)和椭圆\(\dfrac{{{x}^{2}}}{10}+{{y}^{2}}=1\)上的点,则\(P,Q\)两点间的最大距离是\((\) \()\)
已知点\(A(-2,-2),\ \ B(-2,6),\ \ C(4,-2)\),点\(P\)在圆\({{x}^{2}}+{{y}^{2}}=4\)上运动,则\({{\left| PA \right|}^{2}}+{{\left| PB \right|}^{2}}+{{\left| PC \right|}^{2}}\)的最小值为 \((\) \()\)
若圆\(C_{1}\):\((x-1)2+(y+3)^{2}=1\)与圆\(C_{2}\):\((x-a)^{2}+(y-b)^{2}=1\)外离,过直线\(l\):\(x-y-1=0\)上任意一点\(P\)分别做圆\(C_{1}\),\(C_{2}\)的切线,切点分别为\(M\),\(N\),且均保持\(|PM|=|PN|\),则\(a+b=\)( )
如果复数\(z\)满足\(\left|z+3i\right|+\left|z-3i\right|=6 \),那么\(\left|z+1+i\right| \)的最小值是 \((\) \()\)
设\(P\)为双曲线\(C\):\( \dfrac{{x}^{2}}{{a}^{2}}- \dfrac{{y}^{2}}{{b}^{2}}=1(a > 0,b > 0) \)上且在第一象限内的点,\(F_{1}\),\(F_{2}\)分别是双曲线的左、右焦点,\(PF1⊥F1F2\),\(x\)轴上有一点\(A\)且\(AP⊥PF1\),\(E\)是\(AP\)的中点,线段\(EF1\)与\(PF2\)交于点\(M.\)若\(|PM|=2|MF2|\),则双曲线的离心率是\((\) \()\)
进入组卷