求直线l:3x-y=0上,与x轴
解:设圆心是:O(a,b),因为圆心在直线l:3x-y=0上,b=3a
即:O(a,3a),
与x轴相切==>r=b=3a
∴园的方程是:(x-a)^2+(y-3a)^2=(3a)^2------------(1)
把直线x-y=0代入(1)得:
(x-a)^2+(x-3a)^2=9a^2
==>x^2-2ax+a^2+x^2-6ax+9a^2=9a^2
==>2x^2-8ax+a^2=0
==>x1+x2=4a---------------------------------------(2)
==>x1x2=a^2/2----------------------------------...全部
解:设圆心是:O(a,b),因为圆心在直线l:3x-y=0上,b=3a
即:O(a,3a),
与x轴相切==>r=b=3a
∴园的方程是:(x-a)^2+(y-3a)^2=(3a)^2------------(1)
把直线x-y=0代入(1)得:
(x-a)^2+(x-3a)^2=9a^2
==>x^2-2ax+a^2+x^2-6ax+9a^2=9a^2
==>2x^2-8ax+a^2=0
==>x1+x2=4a---------------------------------------(2)
==>x1x2=a^2/2-------------------------------------(3)
被直线x-y=0截得的弦长为2倍根号7
即:(x1-x2)^2+(y1-y2)^2=(2√7)^2【y=x==>{y1=x1,y2=x2}】
==>(x1-x2)^2+(x1-x2)^2=28
==>2(x1+x2)^2-8x1x2-28=0【代入(2),(3)】
==>2*(4a)^2-8*a^2/2-28=0
==>28a^2=28
==>a=±1
==>b=±3
即:圆心O(±1,±3)
所以圆的方程是:(x±1)^2+(y±3)^2=9。
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