过抛物线y^2=-4x的焦点,引倾斜角为120°的直线,交抛物线于A、B两点,求△OAB的面积 .
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/05 22:46:12
![过抛物线y^2=-4x的焦点,引倾斜角为120°的直线,交抛物线于A、B两点,求△OAB的面积 .](/uploads/image/z/6551802-18-2.jpg?t=%E8%BF%87%E6%8A%9B%E7%89%A9%E7%BA%BFy%5E2%3D-4x%E7%9A%84%E7%84%A6%E7%82%B9%2C%E5%BC%95%E5%80%BE%E6%96%9C%E8%A7%92%E4%B8%BA120%C2%B0%E7%9A%84%E7%9B%B4%E7%BA%BF%2C%E4%BA%A4%E6%8A%9B%E7%89%A9%E7%BA%BF%E4%BA%8EA%E3%80%81B%E4%B8%A4%E7%82%B9%2C%E6%B1%82%E2%96%B3OAB%E7%9A%84%E9%9D%A2%E7%A7%AF+.)
xJPoc~=9I9d;$j)*8FHubuRѡMC^JMr[0\;{ZgC6xbD}XuR\eyެƗ$ƪRM-'gI'*v[vJ[;vȳ̭߽""XRd =SJe?8_<P@:OxݝͯFՉRC,R FD1R0(ʗ5H|HAidnb"nc@`
A
ugC~sd{V E[
过抛物线y^2=-4x的焦点,引倾斜角为120°的直线,交抛物线于A、B两点,求△OAB的面积 .
过抛物线y^2=-4x的焦点,引倾斜角为120°的直线,交抛物线于A、B两点,求△OAB的面积 .
过抛物线y^2=-4x的焦点,引倾斜角为120°的直线,交抛物线于A、B两点,求△OAB的面积 .
抛物线y^2=-4x的焦点为:F(-1,0)
AB方程为:y=-√3(x+1)
x=-√3y/3-1
代人y^2=-4x得:
y^2-4√3y/3-4=0
y1+y2=4√3/3,y1y2=-4
(y1-y2)^2=(y1+y2)^2-4y1y2=16/3+16=64/3
|y1-y2|=8√3/3
△OAB的面积=△OAF的面积 + △OFB的面积
=1/2*|OF|*|y1-y2|
=1/2*1*8√3/3
=4√3/3