Bài 1:
\(9x^2+25y^2=225\Leftrightarrow\frac{x^2}{25}+\frac{y^2}{9}=1\)
\(\Rightarrow c^2=a^2-b^2=25-9=16\Rightarrow c=4\Rightarrow F_2\left(4;0\right)\)
Đường thẳng qua \(F_2\) vuông góc trục lớn có pt \(x=4\)
\(\Rightarrow9.4^2+25y^2=225\Leftrightarrow25y^2=81\Rightarrow\left[{}\begin{matrix}y=\frac{9}{5}\\y=-\frac{9}{5}\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}M\left(4;\frac{9}{5}\right)\\N\left(4;-\frac{9}{5}\right)\end{matrix}\right.\)
Bài 2:
Gọi pt elip có dạng \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\)
\(\Rightarrow\left\{{}\begin{matrix}\frac{1}{a^2}+\frac{3}{4b^2}=1\\\frac{0}{a^2}+\frac{1}{b^2}=1\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}b^2=1\\a^2=4\end{matrix}\right.\)
Phương trình elip: \(\frac{x^2}{4}+\frac{y^2}{1}=1\)