Question

急,有分!已知抛物线y2=-x的焦点到准线的距离为1/2,且与直线y=k(x+1)相交于A,B两点,OA垂直于OB.

Answer 1

联立y2=-x和y=k(x+1),A(x1,y1),B(x2,y2)

消x得y^2+y/k-1=0 y1+y2=1/k y1*y2=1

S=1/2|y1-y2|*1=1/2|y1-y2|

=1/2根号[(y1+y2)^2-4y1*y2]

=1/2根号[1/k^2+4]

=根号10

1/k^2+4=40

1/k^2=36

k^2=1/36

k=±1/6