89.

91.

97. $e={\displaystyle \frac{\sqrt{61}}{5}};$ length of the latus rectum: ${\displaystyle \frac{72}{5}}$

99. $e=3;$ length of the latus rectum: 8

103. ${\displaystyle \frac{x^2}{16}}-{\displaystyle \frac{y^2}{20}}=1$

105. ${\displaystyle \frac{y^2}{36}}-{\displaystyle \frac{x^2}{108}}=1$

107. ${\displaystyle \frac{y^2}{5}}-{\displaystyle \frac{x^2}{5}}=1$

109. Points of intersection: $(-{\displaystyle \frac{91}{20}},{\displaystyle \frac{109}{10}})$

111. Points of intersection:

$(-2\sqrt{2},-\sqrt{7}),(-2\sqrt{2},\sqrt{7}),(2\sqrt{2},-\sqrt{7}),(2\sqrt{2},\sqrt{7})$

113. $y={\displaystyle \frac{6}{7}}x-{\displaystyle \frac{5}{7}}$