Question

经过两点M（-3,2√7）,N（-6√2,-7）,焦点在Y轴上的双曲线标准方程是

Answer 1

设双曲线是y^2/a^2-x^2/b^2=1

把M（-3,2√7）,N（-6√2,-7）代入

28/a^2-9/b^2=1

49/a^2-72/b^2=1

28/a^2-9/b^2=1乘以8

224/a^2-72b^2=8

减去49/a^2-72/b^2=1

175/a^2=7

a^2=25,b^2=75

y^2/25-x^2/75=1