Question

Raymond is designing a ceramic pot on a coordinate system where each unit corresponds to 1 millimeter. The neck of the

pot has edges with the shape of a hyperbola, where the asymptotes y = 2.75x and y = -2.75x are followed. If the closest
that any part of the neck edges comes to the center of the neck is 32 millimeters, write an equation for the hyperbola used
to model the edges.

Answer 1

9514 1404 393

Answer:

x^2/1024 -y^2/7744 = 1

Explanation:

The parent hyperbola relation is ...

x^2 -y^2 = 1

This has asymptotes of y = ±x and x-intercepts of ±1.

For the given hyperbola, we want to scale x by a factor of 32, and y by a factor that is 2.75 times that, or 88. Then the equation could be written as ...

(x/32)^2 -(y/88)^2 = 1

More conventionally, the denominator is shown at full value:

x^2/1024 -y^2/7744 = 1