Find the equation of the parabola with its focus at (5,0) and it’s directrix y=2
1 answer:
Answer:
Option A
Step-by-step explanation:
From the question given in the picture attached,
Directrix of the parabola → y = 2
Focus of the parabola → (-5, 0)
Since, focus is below the directrix, parabola will open open downwards.
Equation of the parabola will be in the form of,
y - k = -4p(x - h)²
Here, (h, k) is the vertex of the parabola
p = Distance between vertex and focus or distance between vertex and directrix
Since, distance between vertex and focus = Distance between vertex and directrix
Therefore, vertex of the parabola → (-5, 1)
Now distance (p) between vertex (-5, 0) and focus (-5, 1) = 1 unit
By substituting these values in the equation,
y - 1 = -4(1)[x - (-5)]²
y - 1 = -4(x + 5)²
y = -4(x + 5)² + 1
Option A will be the answer.
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