共50条信息
.如图,在平面直角坐标系\(xOy\)中,点\(A\)\((0,3)\),直线\(l\)\(:\)\(y=\)\(2\)\(x-\)\(4\),设圆\(C\)的半径为\(1\),圆心在\(l\)上.
\((1)\)若圆心\(C\)也在直线\(y=x-\)\(1\)上,过点\(A\)作圆\(C\)的切线,求切线的方程\(;\)
\((2)\)若圆\(C\)上存在点\(M\),使\(|MA|=\)\(2\)\(|MO|\),求圆心\(C\)的横坐标\(a\)的取值范围.
过直线\(l:y=x+1\)上的点\(P\)作圆\(C:(x-1)^{2}+(y-6)^{2}=2\)的两条切线\(l_{1}\),\(l_{2}\),当直线\(l_{1}\),\(l_{2}\)关于直线\(y=x+1\)对称时,\(\left| {PC} \right|=(\) \()\)
已知圆心在\(x\)轴上的圆\(C\)过点\(\left( 0,0 \right)\)和\(\left( -1,1 \right)\),圆\(D\)的方程为\({{\left( x-4 \right)}^{2}}+{{y}^{2}}=4\).
\((\)Ⅰ\()\)求圆\(C\)的方程;
\((\)Ⅱ\()\)由圆\(D\)上的动点\(P\)向圆\(C\)作两条切线分别交\(y\)轴于\(A\),\(B\)两点,求\(\left| AB \right|\)的取值范围.
在直角坐标系\(xOy\)中,以坐标原点为圆心的圆\(O\)与直线\(x-\sqrt{3}y=4\)相切.
\((\)Ⅰ\()\)求圆\(O\)的方程;
\((\)Ⅱ\()\)圆\(O\)与\(x\)轴相交于\(A\),\(B\)两点,圆内的动点\(P\)使\(|PA|\),\(|PO|\),\(|PB|\)成等比数列,求\( \overset{→}{PA}⋅ \overset{→}{PB} \)的取值范围.
圆\({C}_{1} \)的方程为\({x}^{2}+{y}^{2}= \dfrac{4}{25} \),圆\({C}_{2} \)的方程\({(x−\cos θ)}^{2}+{(y−\sin θ)}^{2}= \dfrac{1}{25}(θ∈R) \),过\({C}_{2} \)上任意一点\(P \)作圆\({C}_{1} \)的两条切线\(PM,PN \),切点分别为\(M,N \),则\(∠MPN \)的最大值为
在平面直角坐标系\(xOy\)中,过点\(P(-5,a)\)作圆\(x^{2}+y^{2}-2ax+2y-1=0\)的两条切线,切点分别为\(M(x_{1},y_{1})\),\(N(x_{2},y_{2})\),且\( \dfrac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}+ \dfrac{{x}_{1}+{x}_{2}-2}{{y}_{1}+{y}_{2}} \),则实数\(a\)的值为___________.
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