Step-by-step explanation:
Since the focus is on the right in relation to the directrix, the parabola will open right.
Next, for a parabola opening to the right. the formula is
[tex](y - k) {}^{2} = 4p(x - h)[/tex]
where (h,k) is the vertex.
P is the midpoint of the total distance between the focus and directrix.
Since the parabola is opening right, our vertex and focus will lie on the x axis.
The vertex lies halfway between directrix and focus so the vertex is at
(5,-5).
Note: We choose the point (3,-5) for the directrix because the focus also have (7,-5).
This means p=2.
[tex](y + 5) {}^{2} = 4(2)(x - 5)[/tex]
So our vertex is (5,-5) p=2,
opens right
Answer:
Vertex = (5,-5)
P-value = 2
Opens right
Step-by-step explanation:
Given:
Since focus is on the right side of directrix, it obviously opens right.
Focus for right/left parabola is defined as (h+p,k) and directrix is defined as x = h - p, we’ll be using simultaneous equation for both directrix and focus equation to find vertex and p-value.
[tex]\displaystyle \large{h+p = 7 \to (1)}\\\displaystyle \large{h-p = 3 \to (2)}[/tex]
Solve the simultaneous equation:
[tex]\displaystyle \large{2h=10}\\\displaystyle \large{h=5}[/tex]
Substitute h = 5 in any equation but I’ll choose (1).
[tex]\displaystyle \large{5+p=7}\\\displaystyle \large{p=2}[/tex]
Therefore, from (h,k), the vertex is at (5,-5) and with p-value of 2, since p > 0 then the parabola opens right.