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Vika [28.1K]
3 years ago
7

A mirror with a parabolic cross section is used to collect sunlight on a pipe located at the focus of the mirror. The pipe is lo

cated 7 inches from the vertex of the mirror. Write an equation of the parabola that models the cross section of the mirror. Assume that the parabola opens upward.
A y=1/28x^2
B y=1/42x^2
C y=1/35x^2
D y=1/49x^2
Mathematics
1 answer:
solniwko [45]3 years ago
7 0

Answer:

y= \frac{1}{28} x^2

Step-by-step explanation:

A mirror with a parabolic cross section is used to collect sunlight on a pipe located at the focus of the mirror.

The pipe is located 7 inches from the vertex of the mirror.

The parabola is open upwards . the vertex of the parabola is (0,0)

and pipe is located 7 inches from the vertex (0,0)

7 inches is the focus of the mirror

The distance between the vertex and the focus = 7

Since parabola is upwards and vertex is (0,0) we use formula

4py = x^2

Where p is the distance between the vertex and focus

p = 7 we know

4*7*y = x^2

28y = x^2

Now isolate y by dividing 28 on both sides

y= \frac{1}{28} x^2

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-2x + y = 0 <br><br> -7x + 3y = 2<br> ​
dsp73
This is a system of equations.
First, you set everything in terms of y.
Take the first equation and move set everything equal to y
y=0+2x
Since it’s 0, you don’t need to put it, so
y=2x works.
Then, you plug y=2x into the bottom equation, for the y.
-7x +3(2x)=2. You do this because now you have the same variable for both and it can be solved easily.
Then you can simplify.
-7x+3x = 2
Then combine like terms.
-4x = 2
Divide by -4 on each side.
x = -1/2
So, now that you have x, you can plug in your x-value back into the top equation.
-2(-1/2) + y = 0
Combine like terms
1+y=0
Get y by itself
y=-1
There you have it!
You can check by plugging in both values to any of the equations. We will use the top one here.
-2(-1/2) + (-1) =0
+1 + -1 = 0
It works!
So,
X= -1/2
Y= -1
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