Question

椭圆C:x^2/a^2+y^2/b^2=1的两个焦点(正负1,0),且椭圆上有一点的坐标为(1,3/2)

Answer 1

(1)M到椭圆两焦点的距离之和为10,即2a=10,a=5

离心率为4/5,c=4,b^2=a^2-c^2=5^2-4^2=9,b=3

椭圆方程x^2/25+y^2/9=1

(2)F(c,0)为F(4,0),B(0,3),P(x,y),FT=3

圆有切线PT,满足PF^2=FT^2+PT^2

|PT|=|PB|,PF^2=FT^2+PB^2

(x-4)^2+y^2=3^2+x^2+(y-3)^2

整理得4x-3y+1=0