It describes an hyperbola (option D)
Explanation:
[tex]\frac{(x-1)^2}{20}\text{ + }\frac{(y+2)^2}{16}\text{ = 1}[/tex]
An ellipse is in the form:
[tex]\begin{gathered} \frac{(x-h)^2}{a^2}\text{ + }\frac{(y-k)^2}{b^2}\text{ = 1} \\ \text{This is not similar to the form the equation was given} \end{gathered}[/tex]
A parabola is in the form:
[tex]\begin{gathered} a(x-h)^2=(y-k)^2 \\ \text{vertex form:} \\ y=a(x-h)^2\text{ + k} \\ \text{not similar to the equation we were given} \end{gathered}[/tex]
An equation of circle has a radius in the formula which is not in the given formula. Hence, it can't be circle.
An hyperbola is in the form:
[tex]\begin{gathered} \frac{(x-h)^2}{a^2}\text{ - }\frac{(y-k)^2}{b^2}\text{ = 1} \\ \text{where h = 1, k = -2, a = }\sqrt[]{20},\text{ b = }\sqrt[]{16} \\ \text{this is similar in form to the equation given} \end{gathered}[/tex]
