Question

An asteroid follows a hyperbolic path defined by the equation 16x2 − 9y2 = 576. If one of its foci is the sun's position, the minimum distance between the asteroid and the sun is AU. (Note that x and y are expressed in astronomical units, AU.)

Answer 1

The minimum distance between the asteroid and the sun is 10 - 6 =4


The given hyperbolic path defined as
divide both the sides by 576,



The general equation of

hyperbola is written as
;

Compare with above mention equation
Here

The distance between the asteroid and the sun is seen by figure -1
or
⇒c =10

The minimum distance between the asteroid and the sun is 10 -6 =4