Question

A hyperbola centered at the origin has a vertex at (0,−40) and a focus at (0, 41).

Answer 1

Answer:

y = +/- 40/9 x

NOT 9/40

Step-by-step explanation:

just took the quiz and it was the right answer

Answer 2

$\frac{(x-h)^{2} }{a^{2} } - \frac{(y - k)^{2} }{b^{2} } = 1$

$\frac{(x-0)^{2} }{40^{2} } - \frac{(y - 0)^{2} }{b^{2} } = 1$

a² + b² = c²

40² + b² = 41²

         b² = 41² - 40²

         b² = 1681 - 1600

         b² = 81

         b = 9

slope (m) of asymptote = $+/-\frac{y}{x} = +/-\frac{b}{a} = +/-\frac{9}{40}$

y-intercept (b) = 0 since the center is at the origin

Answer: y = $\frac{9}{40}x$ and y = $-\frac{9}{40}x$