Respuesta :
The equation of a parabola whose vertex is at the origin and whose directrix is y = 3 will be y = 12x².
What is the parabola?
It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.
Let the point (h, k) is the vertex of the parabola and a is the focus.
Then the equation of the parabola will be given as,
y = 4a(x - h)² + k
The vertex of the parabola is at the origin, then the equation of the parabola will be
y = 4a(x - 0)² + 0
y = 4ax²
We know that the distance between the directrix - graph and focus graph is the same.
Then the value of focus will be 3.
Then the equation of the parabola will be
y = 4 × 3 × x²
y = 12x²
The equation of a parabola whose vertex is at the origin and whose directrix is y = 3 will be y = 12x².
More about the parabola link is given below.
https://brainly.com/question/8495504
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