Question

an equation of the hyperbola is
\\( \frac { x ^ { 2 } } { 1 } - \frac { y ^ { 2 } } { 15 } = 1 \\)
(use integers or fractions for any numbers in the expression )
choose the correct graph below
o a.
o b.
o c.
o d.

Explanation:

Step1: Recall the standard form of a hyperbola

The standard form of a hyperbola with a horizontal transverse axis is \(\frac{(x - h)^2}{a^2}-\frac{(y - k)^2}{b^2}=1\), where \((h,k)\) is the center. For the given equation \(\frac{x^2}{1}-\frac{y^2}{15}=1\), the center \((h,k)=(0,0)\), \(a = 1\) (since \(a^2 = 1\)), and \(c^2=a^2 + b^2=1 + 15=16\), so \(c = 4\). The vertices are at \((\pm a,0)=(\pm1,0)\) and foci are at \((\pm c,0)=(\pm4,0)\).

Step2: Analyze the orientation and key - points of the hyperbola

Since the \(x^2\) term is positive, the hyperbola opens left and right (horizontal transverse axis). The vertices are at \((\pm1,0)\).

Answer:

A.