共50条信息
设曲线\(f(x)=\sin x\)在\(x=\dfrac{\pi }{3}\)处的切线与直线\(ax+y+1=0\)垂直，则\(a=\)________．
已知直线\(l\)过点\((-1,2)\)且与直线\(y=\dfrac{2}{3}x\)垂直，则直线\(l\)的方程是\((\) \()\)
已知直线\({{l}_{1}}\)：\(x{\sin }\alpha +y-1=0\)，直线\({{l}_{2}}\)：\(x-3y{\cos }\alpha +1=0\)，若\({{l}_{1}}\bot {{l}_{2}}\)，则\({\sin }2\alpha =(\) \()\)．
\((2)\)求过点\(\left(1,1\right) \)且与圆相切的直线方程．
若曲线\(y{=}e^{x}\)在\(x{=}1\)处的切线与直线\(2x{+}my{+}1{=}0\)垂直，则\(m=(\) \()\)
设曲线\(y= \dfrac{x+1}{x-1} \)在点\(\left(3,2\right) \)处的切线与直线\(ax+y+3=0\)垂直，则\(a=\) ( )
设\(m\in R\)，则“\(m=0\)”是“直线\({{l}_{1}}:\left( m+1 \right)x+\left( 1-m \right)y-1=0\)与直线\({{l}_{2}}:\left( m-1 \right)x+\left( 2m+1 \right)y+4=0\)垂直”的\((\) \()\)
已知直线\(l\)\({\,\!}_{1}\)：\((\)\(m\)\(-2)\)\(x\)\(+3\)\(y\)\(+2\)\(m\)\(=0\)和\(l\)：\(x\)\(+\)\(my\)\(+6=0\)，若\(l\)\({\,\!}_{1}⊥\)\(l\)\({\,\!}_{2}\)，则实数\(m\)的值为( )
若曲线\(y={{x}^{2}}-1\)与\(y=1-{{x}^{3}}\)在\(x={{x}_{0}}\)处的切线互相垂直，则\({{x}_{0}}\)等于\((\) \()\)．
已知直线\(l\)\({\,\!}_{1}\)：\(2\)\(x\)\(-\)\(my\)\(+1=0\)与\(l\)\({\,\!}_{2}\)：\(x\)\(+(\)\(m\)\(-1)\)\(y\)\(-1=0\)，则“\(m\)\(=2\)”是\(l\)\({\,\!}_{1}⊥\)\(l\)\({\,\!}_{2}\)的\((\) \()\)条件．
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