Question

一道参数方程数学题求解答！

已算出来C1：x^2+(y-1)^2=t^2 C2:x^2+y^2/2=1 帮忙算一下第二问

Answer 1

C₁:t=x/cosα t=(y-1)/sinα→x/cosα=(y-1)/sinα→y=tanα·x+1  (t是参数)

C₂:x²=sin²θ y²=1+cos2θ=1+1-2sin²θ→x²+½y²=1

交点：x²+½(tanα·x+1)²=1→令tanα=k

(2+k²)x²+4kx-1=0

x₁+x₂=-4k/(2+k²)、x₁x₂=-1/(2+k²)

(x₁-x₂)²=16k²/(2+k²)²+4/(2+k²)=(20k²+8)/(2+k²)²

|AB|=√[(x₁-x₂)²+(y₁-y₂)²=√[(1+k²)(x₁-x₂)²]=√2

(1+k²)(10k²+4)=(2+k²)²→k=0

∴sinα=0