Question

与椭圆和抛物线相切的直线方程怎么求

Answer 1

y=kx+m

x^2=2py=2p(kx+m)

x^2-2pkx-2pm=0

(-2pk)^2-4*(-2pm)=0.(1)

ax^2+by^2=ab

ax^2+b(kx+m)^2=ab

(a+bk^2)x^2+2bkmx+bm^2-ab=0

(2bkm)^2-4*(a+bk^2)*(bm^2-ab)=0.(2)

(1),(2):

k= m=