True statements are:
- It has a directrix of x = - 4.
- It has a focus at (4, 0).
Step-by-step explanation:
We have the following statements to check on whether it's right or wrong:
1. It has a directrix of x = -4:
According to figure , parabola directrix is at -4 i.e. at x = -4 , Therefore this statement is true!
2. It opens to the left:
In figure, Parabola opens to right not left , Therefore this statement is wrong!
3. It has a vertex at the origin:
Vertex of Parabola is at what points not shown in figure. Therefore this statement cannot be confirmed as true.
4. The axis of symmetry is the y-axis:
Axis of symmetry for above parabola is x-axis as it cuts parabola into two equal halves , y-axis doesn't do this ! Therefore this statement is wrong!
5. It has a focus at (4, 0):
Parabola focus is at [tex]F(4,0)[/tex] on x-axis . And so, Therefore this statement is true!
