Question

Please help, It's for my geometry and I suck at it, there's more that I posted I'll hook you up with points for the help.

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Answer 1

The distance to the focus and the distance directrix of the parabola are;

• Distance to the focus; √((x - 2)² + (y + 4)²)

• Distance to the directrix; |y + 6|

The steps used to find the distances to the focus and directrix are presented as follows;

The coordinate points on the parabola are; (2, -5), (0, -4), and (4, -4)

Therefore, we get the vertex form as follows;

y = a·(x - 2)² + (-5)

y = a·(x - 2)² - 5

When x = 0, we get;

-4 = a·(0 - 2)² - 5

a = 0.25

Therefore; y + 5 = 0.25·(x - 2)²

4×(y + 5) = (x - 2)²

p = 1

The coordinate of the focus is; (h, k + p) = (2, (-5) + 1)

(2, (-5) + 1) = (2, -4)

The focus is; (2, -4)

The directrix is; y = k - p, which is; y = -5 - 1

The directrix is; y = -6

Whereby the focus of the parabola with vertex at (2, -5) is the point (2, -4), and the directrix is the line y = -6, we get;

The distance of the point (x, y), from the

Distance to focus = √((x - 2)² + (y + 4)²)

Distance to directrix is; |y - (-6)| = |y + 6|