Question

The equation of a hyperbola is x^2-4y^2-2x-15=0. What is the width of the asymptote rectangle?

Answer 1

Answer: 8

Explanation:

x² - 2x + ___ - 4y² = 15 + ___

x² - 2x + 1 - 4y² = 15 + 1

(x - 1)² - 4(y)² = 16

`\frac{(x-1)^(2)} {16} - (4(y - 0)^(2))/(16) = (16)/(16)`

`\frac{(x-1)^(2)} {16} - ((y - 0)^(2))/(4) = 1`

`r_(x) = 4`
`r_(y) = 2`

width of rectangle is 2
`(r_(x))` = 2(4) = 8