The true statements for the parabola in the image are:
- C. The point (8, 6) is the same distance from the point (4, 3) as it is from the line y = 1.
How to determine the equation of the directrix?
Mathematically, the standard equation of the directrix lines for a parabola is given by y = a(x - h)² + 2.
Given the following data:
Vertex (h, k) = (4, 3).
Point (x, y) = (8, 6).
Next, we would determine the distance where point (8, 6) lies on the parabola:
y = a(x - h)² + 2
6 = a(8 - 4)² + 2
6 = a(4)² + 2
6 = 16a + 2
16a = 6 - 2
16a = 4
a = 4/16
a = 1/4.
Therefore, the equation becomes:
y = 1/4(x - 4)² + 2
When x = 2, we have:
y = 1/4(2 - 4)² + 2
y = 1/4(-2)² + 2
y = 1/4(4) + 2
y = 1 + 2
y = 3.
In conlusion, the true statements regarding the parabola in the image are:
- The point (8, 6) is the same distance from the point (4, 3) as it is from the line y = 1.
- The point (2, 3) is on the parabola.
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