求方程x2-4xy+5y2-6x+14y+10=0
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解决时间 2021-11-25 05:39
- 提问者网友：凉末
- 2021-11-24 18:29
求方程x2-4xy+5y2-6x+14y+10=0
最佳答案
- 五星知识达人网友：傲气稳了全场
- 2021-11-24 18:59
let A(x1,y1),B(x2,y2) be the intersecion points
x^2+y^2-10x-10y=0 (1)
x^2+y^2+6x-2y-40=0 (2)
(2)-(1)
16x+8y-40=0
2x+y-5=0 (3)
sub (3) into (1)
x^2+(5-2x)^2-10x-10(5-2x)=0
5x^2-10x -25=0
x^2-2x -5 =0
x1+x2 = 2
x1x2= -5
Similary
sub(3) into (1)
[(5-y)/2]^2+y^2-10[(5-y)/2] -10y =0
(5-y)^2+4y^2-20(5-y) -40y =0
5y^2-30y-75=0
y^2-6y-15=0
y1+y2 = 6
y1y2 = -15
(弦长)^2 = (y1-y2)^2+(x1-x2)^2
=(y1+y2)^2+(x1+x2)^2-4y1y2-4x1x2
=36+4+20+60
=120
弦长 = √120 = 2√30
x^2+y^2-10x-10y=0 (1)
x^2+y^2+6x-2y-40=0 (2)
(2)-(1)
16x+8y-40=0
2x+y-5=0 (3)
sub (3) into (1)
x^2+(5-2x)^2-10x-10(5-2x)=0
5x^2-10x -25=0
x^2-2x -5 =0
x1+x2 = 2
x1x2= -5
Similary
sub(3) into (1)
[(5-y)/2]^2+y^2-10[(5-y)/2] -10y =0
(5-y)^2+4y^2-20(5-y) -40y =0
5y^2-30y-75=0
y^2-6y-15=0
y1+y2 = 6
y1y2 = -15
(弦长)^2 = (y1-y2)^2+(x1-x2)^2
=(y1+y2)^2+(x1+x2)^2-4y1y2-4x1x2
=36+4+20+60
=120
弦长 = √120 = 2√30
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