Question

Find the equation of the directrix of the parabola found in part A.

Answer 1

The specific equation of the parabola can be found by plugging the given

values of the variables of the general equation.

Correct Response;

• $\displaystyle The \ equation \ of \ the \ parabolic \ reflector \ is; \ \underline{ y = \frac{1}{12} \cdot x^2}$

Method used to obtain the above equation;

Given parameters;

The vertex of the parabola is at the origin with coordinates (0, 0)

The location of the focus = 3 cm from the vertex

Required:

The equation that models the parabola.

Solution:

The vertex form of the equation of a parabola is y = a·(x - h)² + k

The above equation can be expressed as (x - h)² = 4·p·(y - k)

Where in a vertical parabola;

(h + p, k) = The coordinates of the focus

(h, k) = The coordinates of the vertex = (0, 0)

p = 3 = The distance of the focus from the vertex

Therefore, the coordinates of the focus = (0 + 3, 0) = (3, 0)

The equation of the parabola is therefore;

(x - 0)² = 4×3 × (y - 0) = 12·y

x² = 12·y

• $\displaystyle The \ equation \ of \ the \ parabola \ that \ models \ the \ reflector \ is; \ \underline{ y = \frac{1}{12} \cdot x^2}$

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