Question

直线y=x+1截抛物线y2=2px所得的弦长为二倍根号六,求抛物线方程

Answer 1

y=x+1

x=y-1

y^2=2px=2p*(y-1)

y^2-2px+2p=0

y1+y2=2p,y1*y2=2p

(y1-y2)^2=(x1-x2)^2=(2p)^2-4*2p=4p^2-8p

(x1-x2)^2+(y1-y2)^2=2*(4p^2-8p)=(2√6)^2

(p+1)*(p-3)=0

p=-1,3

y^2=-2x

y^2=6x