The equation that represents the directrix of y² = 12x is x = -3
The parabola is given as:
y² = 12x
The general equation of a parabola is
(y-y₀)² = 4a(x-x₀)
Where the equation of the directrix is x = x₀ - a
By comparing (y-y₀)² = 4a(x-x₀) and y² = 12x, we have:
4a = 12 and x-x₀ = x
Solve for a in 4a = 12
a = 3
Solve for x₀ in x-x₀ = x
x₀ = 0
Substitute a = 3 and x₀ = 0 in x = x₀ - a
x = 0 - 3
Evaluate
x = -3
Hence, the equation that represents the directrix is x = -3
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