Question

The cross section of the reflector in a flashlight is a parabola. Suppose the light bulb is located at the focus of the cross section, 2 cm in front of the vertex.

Assume the vertex is at the origin and that the parabola is concave left (it opens left as depicted in the picture). What is the equation for the cross section of the reflector

Answer 1

Correct answer: y² = - 8 x

Explanation:

The equation of the parabola turned to the left ie to the negative side of the coordinate system is:

y² = - 2 p x where p is the parameter of the parabola

The relationship between the parameter and the focus is.

p = 2 f => p = 2 · 2 = 4 cm

then the equation of the parabola is:

y² = - 2 p x = - 2 · 4 x = - 8 x

y² = - 8 x

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