Question

assignment 7.5: hyperbolas
score: 9/15 answered: 9/15
question 10
write the standard equation for the hyperbola graphed above.
question help: video message instructor

Explanation:

Step1: Identify hyperbola type & center

This is a horizontal hyperbola, centered at $(h,k)=(0,0)$.
Standard form: $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$

Step2: Find $a$ value

Vertices are at $(\pm 2, 0)$, so $a=2$.
$a^2 = 2^2 = 4$

Step3: Find $b$ value

Asymptotes are $y=\pm 2x$, so $\frac{b}{a}=2$.
$b = 2a = 2*2=4$, $b^2=4^2=16$

Step4: Substitute into standard form

Plug $a^2=4$, $b^2=16$ into the equation.

Answer:

$\frac{x^2}{4} - \frac{y^2}{16} = 1$