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4. (5 分) 圆 $x^{2}+y^{2}-2 x-8 y+13=0$ 的圆心到直线 $a x+y-1=0$ 的距离为 1 , 则 $a=($

Gaokao · Math · previous-year question

  1. A.$-\frac{4}{3}$correct
  2. B.$-\frac{3}{4}$
  3. C.$\sqrt{3}$
  4. D.2

Answer

A. $-\frac{4}{3}$

Explanation

解：圆 $x^{2}+y^{2}-2 x-8 y+13=0$ 的圆心坐标为: $(1,4)$, 故圆心到直线 $a x+y-1=0$ 的距离 $d=\frac{|a+4-1|}{\sqrt{a^{2}+1}}=1$, 解得: $a=-\frac{4}{3}$, 故选: A.

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