如图,从圆C:x²+y²-4x-6y+12=0外一点P(a,b)向圆引切线PT,T为切点,且PT=PO(O为原点)求PT的最小值及此刻P的坐标
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/11 18:26:47
![如图,从圆C:x²+y²-4x-6y+12=0外一点P(a,b)向圆引切线PT,T为切点,且PT=PO(O为原点)求PT的最小值及此刻P的坐标](/uploads/image/z/5260915-19-5.jpg?t=%E5%A6%82%E5%9B%BE%2C%E4%BB%8E%E5%9C%86C%EF%BC%9Ax%26%23178%3B%2By%26%23178%3B-4x-6y%2B12%3D0%E5%A4%96%E4%B8%80%E7%82%B9P%EF%BC%88a%2Cb%29%E5%90%91%E5%9C%86%E5%BC%95%E5%88%87%E7%BA%BFPT%2CT%E4%B8%BA%E5%88%87%E7%82%B9%2C%E4%B8%94PT%3DPO%28O%E4%B8%BA%E5%8E%9F%E7%82%B9%EF%BC%89%E6%B1%82PT%E7%9A%84%E6%9C%80%E5%B0%8F%E5%80%BC%E5%8F%8A%E6%AD%A4%E5%88%BBP%E7%9A%84%E5%9D%90%E6%A0%87)
xRN@SitHHE&0D7#*>I! #G!R쐰}=/k*{qPOEN7e 5(PۖPqY]if̙L-v+bZ`JpEU",Uܓ盲R5^vO_hP{HeK?EE$jP3-pBM!Hj!UdupL86I3iC <ԙKbػX efJ#2yJa٬~,ƚ)Se7SF>8T:LY5~E
如图,从圆C:x²+y²-4x-6y+12=0外一点P(a,b)向圆引切线PT,T为切点,且PT=PO(O为原点)求PT的最小值及此刻P的坐标
如图,从圆C:x²+y²-4x-6y+12=0外一点P(a,b)向圆引切线PT,T为切点,且PT=PO(O为原点)
求PT的最小值及此刻P的坐标
如图,从圆C:x²+y²-4x-6y+12=0外一点P(a,b)向圆引切线PT,T为切点,且PT=PO(O为原点)求PT的最小值及此刻P的坐标
圆C:(x-2)^2+(y-3)^2=1, 圆心C为(2,3)
CPT构成直角三角形,因此PT^2=PC^2-CT^2=(a-2)^2+(b-3)^2-1=a^2-4a+b^2-6b+12
因为PT=PO,
所以a^2-4a+b^2-6b+12=a^2+b^2
因此2a+3b=6, a=3-3/2b
PT最小值,即a^2-4a+b^2-6b+12最小值,将a=3-3/2b代入
可得:13/4b^2-9b+9
当b=18/13时,13/4b^2-9b+9有最小值为36/13
因此PT最小值为6根号13/13, P的坐标为(12/13,18/13)