Use the information provided to write the standard form equation of each hyperbola.
1) \( -x^{2}+y^{2}-18 x-14 y-132=0 \)
2) \( 9 x^{2}-4 y^{2}-90 x+32 y-163=0 \)
\[
\frac{(y-7)^{2}}{100}-\frac{(x+9)^{2}}{100}=1 \quad \frac{(x-5)^{2}}{36}-\frac{(y-4)^{2}}{81}=1
\]
3) \( -16 x^{2}+9 y^{2}+32 x+144 y-16=0 \)
4) \( -2 x^{2}+3 y^{2}+4 x-60 y+268=0 \)
\[
\frac{(y+8)^{2}}{64}-\frac{(x-1)^{2}}{36}=1 \quad \frac{(y-10)^{2}}{10}-\frac{(x-1)^{2}}{15}-1
\]
5)
\[
\frac{x^{2}}{25}-\frac{(y-1)^{2}}{16}=1
\]
7) Vertices: \( (8,14),(8,-10) \)
Conjugate Axis is 6 units long
\[
\frac{\left(\begin{array}{ll}
y & 2
\end{array}\right)^{2}}{144}-\frac{\left(\begin{array}{ll}
x & 8
\end{array}\right)^{2}}{9}=1
\]
9) Vertices: \( (15,1),(-1,1) \)
Endpoints of Conjugate Axis: \( (7,7) \) \( (7,-5) \)
\[
\frac{\left(\begin{array}{ll}
x & 7
\end{array}\right)^{2}}{64}-\frac{\left(\begin{array}{ll}
y & 1
\end{array}\right)^{2}}{36}=1
\]
\( 6) \)
\[
\frac{\left(\begin{array}{ll}
y & 2
\end{array}\right)^{2}}{4}-\frac{x^{2}}{25}=1
\]
8) Vertices: \( (4,9+\sqrt{30}),(4,9-\sqrt{30}) \) Conjugate Axis is \( 2 \sqrt{195} \) units long
\[
\frac{(y-9)^{2}}{30}-\frac{(x-4)^{2}}{195}=1
\]
10) Vertices: \( \left(-2, \frac{5}{2}\right),\left(-16, \frac{5}{2}\right) \)
Fndprints of Conjugate Axis: \( \left(-9, \frac{15}{2}\right) \) \( \left(-9,-\frac{5}{2}\right) \)
\[
\frac{(x+9)^{2}}{49}-\frac{\left(y \frac{5}{2}\right)^{2}}{25}=1
\]
