Write the equation of the hyperbola with center left-parenthesis 2 comma negative 5 right-parenthesis, vertex left-parenthesis 2 comma negative 2 right-parenthesis, and focus left-parenthesis 2 comma negative 5 plus 2 Start Root 3 End Root right-parenthesis.
(1 point)
Responses
Start Fraction left-parenthesis y plus 5 right-parenthesis squared over 9 End Fraction minus Start Fraction left-parenthesis x minus 2 right-parenthesis squared over 3 End Fraction equals 1
Image with alt text: Start Fraction left-parenthesis y plus 5 right-parenthesis squared over 9 End Fraction minus Start Fraction left-parenthesis x minus 2 right-parenthesis squared over 3 End Fraction equals 1
Start Fraction left-parenthesis y plus 5 right-parenthesis squared over 9 End Fraction minus Start Fraction left-parenthesis x minus 2 right-parenthesis squared over 12 End Fraction equals 1
Image with alt text: Start Fraction left-parenthesis y plus 5 right-parenthesis squared over 9 End Fraction minus Start Fraction left-parenthesis x minus 2 right-parenthesis squared over 12 End Fraction equals 1
Start Fraction left-parenthesis y plus 5 right-parenthesis squared over 3 End Fraction minus Start Fraction left-parenthesis x minus 2 right-parenthesis squared over 9 End Fraction equals 1
Image with alt text: Start Fraction left-parenthesis y plus 5 right-parenthesis squared over 3 End Fraction minus Start Fraction left-parenthesis x minus 2 right-parenthesis squared over 9 End Fraction equals 1
Start Fraction left-parenthesis y plus 5 right-parenthesis squared over 12 End Fraction minus Start Fraction left-parenthesis x minus 2 right-parenthesis squared over 9 End Fraction equals 1
Image with alt text: Start Fraction left-parenthesis y plus 5 right-parenthesis squared over 12 End Fraction minus Start Fraction left-parenthesis x minus 2 right-parenthesis squared over 9 End Fraction equals 1
The equation of the hyperbola is:
\[ \frac{{(y+5)^2}}{9} - \frac{{(x-2)^2}}{3} = 1 \]