Your new flashlight uses a parabolic mirror which can be modeled by the equation (x – 2)² = 5(y + 1), where x and y are measured
in centimeters. You need to place a new light bulb in your flashlight. How far away from the vertex of the parabolic mirror should you place the bulb to ensure a perfect beam of light?
2 answers:
The given equation is
(x - 2)² = 5(y + 1).
The given equation for the parabola is in the standard form
(x - h)² = 4p(y - k)
where
h = 2
4p = 5, so that p = 5/4
k = -1
The vertex is at
(h,k) or (2, -1)
The focus is located at
(h, k + p) or (2, -1 + 5/4) = (2, 1/4)
We should place the bulb at p = 5/4 from the vertex.
Answer: 1 1/4 or 1.25 cm
(x - 2)² = 5(y + 1).
The given equation for the parabola is in the standard form
(x - h)² = 4p(y - k)
where
h = 2
4p = 5, so that p = 5/4
k = -1
The vertex is at
(h,k) or (2, -1)
The focus is located at
(h, k + p) or (2, -1 + 5/4) = (2, 1/4)
We should place the bulb at p = 5/4 from the vertex.
Answer: 1 1/4 or 1.25 cm
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Answer:
A
Step-by-step explanation:
This is how I write
y=kx+m
but I have seen some write it like this:
y=mx+b
Well both of them are the same thing, I'll use the first one because I'm more comfortable with it.
y=kx+m
To find out what k
So you first need to choose two points.
I'll go for (0,-5) and (2,0)
Now you could insert k into the equation and it will look like this.
To find out what m is just pick one point and insert it into the equation. So if I pick (0,-5). 0=X therefore it should be replaced by x and -5=y therefore it should also be replaced by y.
m=-5
Try it with another point to see if you get the same answer. this time I'll pick (-6,10)
m= -5
The equation will be y=-5/2x-5)