List all the multiples of the numbers:
2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100
5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100
6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96
9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99
The least common multiple of 2, 5, 6, and 9 is 90.
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.