NZ Level 8 (NZC) Level 3 (NCEA) [In development]

Applications of hyperbolas

The physicist Ernest Rutherford discovered that when alpha particles are directed towards the nuclei of gold atoms, they are eventually deflected along hyperbolic paths.

If a particle can get as close as $8$8 units to the nucleus along a hyperbolic path with an asymptote given by $y=\frac{1}{4}x$`y`=14`x`, what is the equation of its path?

Loading Graph...

Easy

Approx 5 minutes

Sign up to try all questions

Apply the geometry of conic sections

Form and use trigonometric, polynomial, and other non-linear equations

Apply the geometry of conic sections in solving problems

Apply trigonometric methods in solving problems