Answer:
Option D
Step-by-step explanation:
Let's explain why the Option D is correct :
- The Parabola equation: [tex]$x \leq y^2 - 8$[/tex]
This is a parabola equation with vertex at x = -8.
Despite that the "traditional equation" is [tex]$ y=x^2 + b $[/tex] in this case the parabola equation is plotted in the X axis and has a [tex]$ <= $[/tex] sign which indicates that X will take values less and equal than [tex]$ y^2 -8 $[/tex]
The graph of the parabola is attached to the answer.
- The hyperbola equation: [tex]$ {x^2 /{3^2}} - {y^2 / {5^2}} > 1 $[/tex]
This is a hyperbola equation with center at (0,0) and vertex's : V1=(3;0) and V2=(-3;0)
The two points (0;5) and (0;-5) on the Y axis are not on the hyperbola.
It's similar to the previous case of the parabola, Despite that the "traditional equation" of the Hyperbola : [tex]$ {x^2 /{a^2}} - {y^2 / {b^2}} = 1 $[/tex] in this case the hyperbola equation has a [tex]$ > $[/tex] sign which indicates that hyperbola will take values greater than those who correspond to [tex]$ {x^2 /{3^2}} - {y^2 / {5^2}} = 1 $[/tex]
The graph of the Hyperbola is also attached
Finally we deduce that the D system of inequalities is the correct one.
Also the answer is attached.
