一道英文数学题求救!a tangent line to the eclipse x^2+4y^2=5 has an x-

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一道英文数学题求救!
a tangent line to the eclipse x^2+4y^2=5 has an x-intercept of -5 and passes through the point Q(3,k) in the first quadrant.Determine the value of k

答：
与椭圆x²+4y²=5相切的直线在x轴上的截距为-5
并且经过点（3,k）,试求k值
设直线为y=a(x+5),在x轴上的截距为-5
代入椭圆方程得：
x²+4a²(x²+10x+25)=5
整理得：
(4a²+1)x²+40a²x+100a²-5=0
直线与椭圆仅有一个交点为切点,上述方程有唯一的解
判别式=(40a²)²-4(4a²+1)(100a²-5)=0
所以：1600a^4-1600a^4+80a²-400a²+20=0
所以：320a²=20
解得：a²=1/16
所以：a=1/4或者a=-1/4
直线为y=(x+5)/4或者y=-(x+5)/4
x=3代入得：y=k=2或者-2
所以：k=2或者k=-2 再答：有人恶心到一字不漏复制！

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