已知椭圆C:x2/a2+y2/b2=1的两个焦点为F1(-1,0)F2(1,0)并且经过M(1,3/2)求椭圆C的标准方

1)、c=1,a^2=b^2+c^2=b^2+1.2)、椭圆去分母,a^2b^2=b^2x^2+a^2y^2.M代入,a^2b^2=b^2+(9/4)a^2,99a^2b^2=4b^2+9a^2.前式代入,4b^2(b^2+1)=4b^2+9(b^2+1),4b^4+4b^2=4b^2+9b^2+9,4b^4-9b^2=9,[2b^2-(9/4)]^2=9+(9/4)^2=9x25/16.同开方,2b^2-(9/4)=3x5/4(已舍负值),2b^2=(9/4)+(15/4)=24/4=6,b^2=3.3)、a^2=3+1=4,(x^2/4)+(y^2/3)=1.

X2+9Y2/4=1

(x2)/4 (y2)/3=1　望采纳！