双曲线c：x²/a² -y²/b²=1离心率=2它一个焦点到渐近线距离为根号3，求双曲线c标准方程 已知双曲线方程C：x²／a²－y...
\u5df2\u77e5\u53cc\u66f2\u7ebfC\uff1ax²\uff0fa²\uff0dy²\uff0fb²=1\u7684\u7126\u8ddd\u4e3a4\uff0c\u4ee5\u539f\u70b9\u4e3a\u5706\u5fc3\u56e0\u4e3a\u5176\u4e2d\u4e00\u6761\u51c6\u7ebf\u7684\u65b9\u7a0b\u4e3ax\uff1d3\uff0f2\uff0c\u6240\u4ee5\u6211\u4eec\u53ef\u5f97\u51faa\uff1eb\u3002\u79bb\u5fc3\u7387\u4e3ac/a\uff0c\u51c6\u7ebf\u4e3aa2/c=3\uff0f2\uff0c\u90a3\u4e48a2=3\uff0cc=2\u3002\u6240\u4ee5b=1\uff0c\u6240\u4ee5\u53cc\u66f2\u7ebf\u65b9\u7a0b\u4e3ax²\uff0f3\uff0dy²\uff1d1
双曲线C：x²/a² -y²/b²=1离心率c/a=2,所以c=2a,①
焦点(2a,0)到渐近线x/a-y/b=0的距离2/√[(1/a)^2+(1/b^2)]=√3，
所以2ab/c=√3，b=√3，
由①，√(a^2+3)=2a,
平方得a^2+3=4a^2,a^2=1,
所以双曲线C的方程是x^2-y^2/3=1.
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