Answer:
The minimum distance between the asteroid and the sun is 10 - 6 =4
Step-by-step explanation:
The given hyperbolic path defined as [tex]16x^{2}-9y^{2}=576[/tex]
divide both the sides by 576,
[tex]\frac{16x^{2}}{576}-\frac{9y^{2}}{576}=\frac{576}{576}[/tex]
[tex]\frac{x^{2}}{36}-\frac{y^{2}}{64}=1[/tex]
[tex]\frac{x^{2}}{36}-\frac{y^{2}}{64}=1[/tex]
The general equation of hyperbola is written as
;
[tex]\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1[/tex]
Compare [tex]\frac{x^{2}}{36}-\frac{y^{2}}{64}=1[/tex] with above mention equation
Here [tex]a^{2}=36 \ \text{and} \ b^{2}=64[/tex]
The distance between the asteroid and the sun is seen by figure -1
[tex]c^{2}=a^{2}+b^{2}=100[/tex] or [tex]c^{2}=100[/tex]
⇒c =10
The minimum distance between the asteroid and the sun is 10 -6 =4
