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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 2 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.

Respuesta :

An equation of the parabola that models the cross section of the mirror is y = 1/8 × x² I am hoping that this answer has satisfied your query and it will be able to help you in your endeavor, and if you would like, feel free to ask another question.

JeanaShupp

Answer: [tex]x^2=8y[/tex]


Step-by-step explanation:

Let the given parabolic mirror opens upwards and vertex=(0,0)

Focus point of the parabolic mirror is located 2 inches from the vertex of the mirror.  ∴ p=2

Since, the parabola opens upward, then the equation of the parabola is of the form [tex]x^2=4py[/tex]

Substitute the value of p=2 in this, we get the equation of the parabolic mirror

[tex]x^2=4(2)y\\\Rightarrow\ x^2=8y[/tex]

Hence, the equation of the parabola that models the cross section of the mirror is [tex]x^2=8y[/tex]

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