Answer:
[tex]\frac{y^2}{4}-\frac{x^2}{117}=1[/tex]
Step-by-step explanation:
The standard form of hyperbola centered at origin is given by:
[tex]\frac{y^2}{a^2}-\frac{x^2}{b^2}=1[/tex] ....[1]
where,
vertices and foci are [tex](0, \pm a)[/tex] and [tex](0, \pm c)[/tex] respectively.
As per the statement:
The hyperbola with vertices at (0, ±2) and foci at (0, ±11).
⇒a = 2 and c = 11
⇒[tex]a^2 = 4[/tex] and [tex]c^2 = 121[/tex]
To find [tex]b^2[/tex]:
Using the equation:
[tex]b^2 = c^2-a^2[/tex]
then;
[tex]b^2 = 11^2-2^2 = 121-4 = 117[/tex]
⇒[tex]b^2 = 117[/tex]
Substitute the given values in [1] we have;
[tex]\frac{y^2}{4}-\frac{x^2}{117}=1[/tex]
Therefore, an equation in standard form for the hyperbola with vertices at (0, ±2) and foci at (0, ±11) is, [tex]\frac{y^2}{4}-\frac{x^2}{117}=1[/tex]
