The specific equation of the parabola can be found by plugging the given
values of the variables of the general equation.
Correct Response;
- [tex]\displaystyle The \ equation \ of \ the \ parabolic \ reflector \ is; \ \underline{ y = \frac{1}{12} \cdot x^2}[/tex]
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
- [tex]\displaystyle The \ equation \ of \ the \ parabola \ that \ models \ the \ reflector \ is; \ \underline{ y = \frac{1}{12} \cdot x^2}[/tex]
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