忘写题目了:1.已知A,B为椭圆x^2/a^2+25y^2/9a^2=1上两点,F2为右焦点,若AF2+BF2=8/5a,AB中点到椭圆左准线的距离为3/2,求该椭圆方程。2.过椭圆C:x^2/8+y^2/4=1上的一点P(x0,y0)向圆x^2+y^2=4引两条切线PA
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![忘写题目了:1.已知A,B为椭圆x^2/a^2+25y^2/9a^2=1上两点,F2为右焦点,若AF2+BF2=8/5a,AB中点到椭圆左准线的距离为3/2,求该椭圆方程。2.过椭圆C:x^2/8+y^2/4=1上的一点P(x0,y0)向圆x^2+y^2=4引两条切线PA](/uploads/image/z/3821715-27-5.jpg?t=%E5%BF%98%E5%86%99%E9%A2%98%E7%9B%AE%E4%BA%86%EF%BC%9A1.%E5%B7%B2%E7%9F%A5A%2CB%E4%B8%BA%E6%A4%AD%E5%9C%86x%5E2%2Fa%5E2%2B25y%5E2%2F9a%5E2%3D1%E4%B8%8A%E4%B8%A4%E7%82%B9%EF%BC%8CF2%E4%B8%BA%E5%8F%B3%E7%84%A6%E7%82%B9%EF%BC%8C%E8%8B%A5AF2%2BBF2%3D8%2F5a%EF%BC%8CAB%E4%B8%AD%E7%82%B9%E5%88%B0%E6%A4%AD%E5%9C%86%E5%B7%A6%E5%87%86%E7%BA%BF%E7%9A%84%E8%B7%9D%E7%A6%BB%E4%B8%BA3%2F2%EF%BC%8C%E6%B1%82%E8%AF%A5%E6%A4%AD%E5%9C%86%E6%96%B9%E7%A8%8B%E3%80%822.%E8%BF%87%E6%A4%AD%E5%9C%86C%3Ax%5E2%2F8%2By%5E2%2F4%3D1%E4%B8%8A%E7%9A%84%E4%B8%80%E7%82%B9P%EF%BC%88x0%2Cy0%29%E5%90%91%E5%9C%86x%5E2%2By%5E2%3D4%E5%BC%95%E4%B8%A4%E6%9D%A1%E5%88%87%E7%BA%BFPA)
忘写题目了:1.已知A,B为椭圆x^2/a^2+25y^2/9a^2=1上两点,F2为右焦点,若AF2+BF2=8/5a,AB中点到椭圆左准线的距离为3/2,求该椭圆方程。2.过椭圆C:x^2/8+y^2/4=1上的一点P(x0,y0)向圆x^2+y^2=4引两条切线PA
忘写题目了:
1.已知A,B为椭圆x^2/a^2+25y^2/9a^2=1上两点,F2为右焦点,若AF2+BF2=8/5a,AB中点到椭圆左准线的距离为3/2,求该椭圆方程。
2.过椭圆C:x^2/8+y^2/4=1上的一点P(x0,y0)向圆x^2+y^2=4引两条切线PA,PB。A,B为切点,如直线AB与X轴,Y轴交与M,N两点
(1)若向量PAx向量PB=0,求P坐标
(2)求直线AB的方程
(3)求三角形MON面积最小值.
忘写题目了:1.已知A,B为椭圆x^2/a^2+25y^2/9a^2=1上两点,F2为右焦点,若AF2+BF2=8/5a,AB中点到椭圆左准线的距离为3/2,求该椭圆方程。2.过椭圆C:x^2/8+y^2/4=1上的一点P(x0,y0)向圆x^2+y^2=4引两条切线PA
b^2=9a^2/25
1
c^2=16a^2/25
b=3a/5,c=4a/5
F2(c,0)
AF2=a-e*Ax
BF2=a-eBx
AF2+BF2=2a-e*(Ax+Bx)=8a/5 2a/5=(4/5)(Ax+Bx) Ax+Bx=a/2
(Ax+Bx)/2+a^2/c=a/4+a^2/(4a/5)=3a^2/2=3/2 a=1
x^2+y^2/(9/25)=1
2
PA=PB
PA*PB=0,PA垂直PB,OA垂直OB
OP=√(OA^2+OB^2)=2√2
x^2+y^2=8
x^2/8+y^2/4=1
x^2/2+y^2=4
x^2/2=4
x=2√2,y=0 或x=-2√2,y=0
P(2√2,0) P(-2√2,0)
PA斜率1 PA斜率-1
PB斜率-1 PB斜率1
AB垂直平分OP
AB直线
x=√2 x=-√2