Question

椭圆 (9 19:35:1)已知椭圆 C：y^2/a^2+x^2/b^2=1(a大于b大于0)的右顶点为A(1,0),过

Answer 1

右顶点为A(1,0)

所以b=1

y^2/a^2+x^2=1

c^2=a^2-b^2=a^2-1

则过c的焦点且垂直长轴的直线是y=c=√(a^2-1)

代入椭圆

(a^2-1)/a^2+x^2=1

x^2=1-(a^2-1)/a^2=1/a^2

x1=1/a,x2=-1/a

所以弦长=1/a-(-1/a)=1

a=2

所以y^2/4+x^2=1