已知抛物线C₁的焦点与椭圆C2:x²/6+y²/5=1的右焦点重合,抛物线C₁的顶点在坐标原点,过点M(4,0)的直线l与抛物线C₁分别教育A,B两点,求三角形AOB面积的最小值?
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![已知抛物线C₁的焦点与椭圆C2:x²/6+y²/5=1的右焦点重合,抛物线C₁的顶点在坐标原点,过点M(4,0)的直线l与抛物线C₁分别教育A,B两点,求三角形AOB面积的最小值?](/uploads/image/z/2490382-46-2.jpg?t=%E5%B7%B2%E7%9F%A5%E6%8A%9B%E7%89%A9%E7%BA%BFC%26%238321%3B%E7%9A%84%E7%84%A6%E7%82%B9%E4%B8%8E%E6%A4%AD%E5%9C%86C2%3Ax%26%23178%3B%2F6%2By%26%23178%3B%2F5%3D1%E7%9A%84%E5%8F%B3%E7%84%A6%E7%82%B9%E9%87%8D%E5%90%88%2C%E6%8A%9B%E7%89%A9%E7%BA%BFC%26%238321%3B%E7%9A%84%E9%A1%B6%E7%82%B9%E5%9C%A8%E5%9D%90%E6%A0%87%E5%8E%9F%E7%82%B9%2C%E8%BF%87%E7%82%B9M%EF%BC%884%2C0%EF%BC%89%E7%9A%84%E7%9B%B4%E7%BA%BFl%E4%B8%8E%E6%8A%9B%E7%89%A9%E7%BA%BFC%26%238321%3B%E5%88%86%E5%88%AB%E6%95%99%E8%82%B2A%2CB%E4%B8%A4%E7%82%B9%2C%E6%B1%82%E4%B8%89%E8%A7%92%E5%BD%A2AOB%E9%9D%A2%E7%A7%AF%E7%9A%84%E6%9C%80%E5%B0%8F%E5%80%BC%3F)
已知抛物线C₁的焦点与椭圆C2:x²/6+y²/5=1的右焦点重合,抛物线C₁的顶点在坐标原点,过点M(4,0)的直线l与抛物线C₁分别教育A,B两点,求三角形AOB面积的最小值?
已知抛物线C₁的焦点与椭圆C2:x²/6+y²/5=1的右焦点重合,抛物线C₁的顶点在坐标原
点,过点M(4,0)的直线l与抛物线C₁分别教育A,B两点,求三角形AOB面积的最小值?
已知抛物线C₁的焦点与椭圆C2:x²/6+y²/5=1的右焦点重合,抛物线C₁的顶点在坐标原点,过点M(4,0)的直线l与抛物线C₁分别教育A,B两点,求三角形AOB面积的最小值?
椭圆C2:x²/6+y²/5=1的右焦点 F2(1,0)
已知抛物线C₁的焦点与椭圆C2:x²/6+y²/5=1的右焦点重合,抛物线C₁的顶点在坐标原点
p/2=1 2p=4
抛物线C₁方程为y^2=4x
设直线方程为 x=my+4
y^2=4my+16
y^2-4my-16=0
设A(x1,y1) B(x2,y2)
y1+y2=4m y1y2=-16
|y1-y2|=√[(y1+y2)^2-4y1y2]=√[16m^2+64]=4√(m^2+4)
S△ABO=S△AOM+S△BOM=1/2*|OM|*|y1|+1/2*|OM|*|y2|
=1/2*|OM|*(|y1|+|y2|)
=2|y1-y2|
=8√(m^2+4) 当m^2=0时
三角形AOB面积的最小值Smin=16