a为何值时,两圆x^2+y^2-2ax+4y+a^2-5=0和x^2+y^2-2x-2ay+a^2-3=0 外切?
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a为何值时,两圆x^2+y^2-2ax+4y+a^2-5=0和x^2+y^2-2x-2ay+a^2-3=0 外切?
![a为何值时,两圆x^2+y^2-2ax+4y+a^2-5=0和x^2+y^2-2x-2ay+a^2-3=0 外切?](/uploads/image/z/1992-48-2.jpg?t=a%E4%B8%BA%E4%BD%95%E5%80%BC%E6%97%B6%2C%E4%B8%A4%E5%9C%86x%5E2%2By%5E2-2ax%2B4y%2Ba%5E2-5%3D0%E5%92%8Cx%5E2%2By%5E2-2x-2ay%2Ba%5E2-3%3D0+%E5%A4%96%E5%88%87%3F)
x²+y²-2ax+4y+a²-5=0
(x - a)² + (y + 2)² = 9,圆心A(a,-2),半径R = 3
x²+y²-2x-2ay+a²-3=0
(x -1)² + (y -a)² = 4,圆心B(1,a),半径r = 2
二者外切,AB = R+r = 5
AB² = 25 = (a - 1)² + (-2 - a)² = 2a² + 6a + 5
a² + 3a - 10 = 0
(a + 5)(a - 2) = 0
a = -5或a = 2
(x - a)² + (y + 2)² = 9,圆心A(a,-2),半径R = 3
x²+y²-2x-2ay+a²-3=0
(x -1)² + (y -a)² = 4,圆心B(1,a),半径r = 2
二者外切,AB = R+r = 5
AB² = 25 = (a - 1)² + (-2 - a)² = 2a² + 6a + 5
a² + 3a - 10 = 0
(a + 5)(a - 2) = 0
a = -5或a = 2
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