参数方程大题
发布网友
发布时间：2022-07-13 00:43
共1个回答
热心网友
时间：2023-10-21 18:04
(1) x=1/2t
t=2x
y=3-t
=3-2x
C：y=3-2x............(1)
ρ(1+sinθ)=2
ρ+ρsinθ=2
√(x^2+y^2)+y=2
√(x^2+y^2)=2-y
x^2+y^2=4-4y+y^2
D：x^2=4-4y..........(2)
(2) (1)代入(2)：x^2=4-4(3-2x)
x^2-8x=-8
(x-4)^2=-8+16
(x-4)^2=8
x-4=±2√2
x=4±2√2
x1=4-2√2
y1=3-2(4-2√2)
=-5+4√2
M(4-2√2,-5+4√2)
x2=4+2√2
y2=3-2(4+2√2)
=-5-4√2
N(4+2√2,-5-4√2)
|MN|=√[(4-2√2-4-2√2)^2+(-5+4√2+5+4√2)^2]
=√[32+128]
=√160
=4√10
