Question

Help Please

Answer 1

I believe the answer is c. hope this helps

Answer 2

If a hyperbola is centered at the origin and has vertex and focus on the x-axis, then its equation is

$\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1.$

1. The vertex A of hyperbola has coordinates (-6,0), then the distance from the origin (center of the hyperbola) to the vertex is

$a=6.$

2. The focus F has coordinates (10,0), then the distance from the origin to the focus is

$c=10.$

3. Find b, using formula $c^2=a^2+b^2:$

$10^2=6^2+b^2,\\ \\b^2=100-36=64,\\ \\b=8.$

4. The equation of the hyperbola is

$\dfrac{x^2}{36}-\dfrac{y^2}{64}=1.$

5. The directrices' equations are

$x=-\dfrac{a}{e},\ x=\dfrac{a}{e},$

where $e=\dfrac{c}{a}.$

In your case,

$e=\dfrac{10}{6}$

and directrices' equations are

$x=-\dfrac{6}{\frac{10}{6}}=-3.6,\ x=\dfrac{6}{\frac{10}{6}}=3.6.$

Answer: x=-3.6, x=3.6, correct choice is C