Question

设长轴长为4的椭圆C:x /a +y /b =1(a>b>0)的左右焦点分别为F1.F2,左右顶点为A.B,上顶点为N,

Answer 1

y(0) = c = -3

y(3) = 9a 3b - 3 = 0

AO/OC = 1/3, A(-1,0)

y(-1) = a-b-3 = 0

a = b 3

9(b 3) 3b-3 = 0

b = -2

y = x^2 -2x - 3

D(2,-3)

设M坐标为(x,0)

tanMND = tan(180-MNA) =-12/5

要求角BMD=MND

tan BMD = -tanAMD = (x-1)/3 = 12/5

x = 41/5 > B点x 坐标

所以M不存在,T不存在