Question

The parabola in the image has its focus at (4,3).Its directrix is the line y=1.The point (8,6) is on the parabola.

Answer 1

The statements that are true for this parabola are:

C. The point (8, 6) is the same distance from the point (4, 3) as it is from the line y = 1.

Option D.

Given the following data:

• Vertex (h, k) = (4, 3).

• Point (x, y) = (8, 6).

How to determine the equation of the directrix?

Mathematically, the standard equation of the directrix line for a parabola is given by: y = a(x - h)² + 2.

Next, we would determine the distance where point (8, 6) lie on the parabola as follows:

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 parabolic 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 statements that are true for this parabola in the image above include:

• The point (8, 6) is the same distance from the point (4, 3) as it is from line (y = 1).

• The point (2, 3) is on the parabola.

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