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Chapter 7: Problem 70

Explain how to use \(y^{2}=8 x\) to find the parabola's focus and directrix.

Short Answer

Expert verified
The focus of the parabola is located at (2, 0) and its directrix is \(x = -2\).

Step by step solution

01

Identify the Vertex

In our case, the equation is rewritten as \((y-0)^2 = 2(4)(x-0)\). Hence, by comparing this to the standard form, it can be seen that the vertex h = 0 and k = 0, so the vertex is (0,0).
02

Identify the value of 'a'

Once the vertex is determined, next we need the value of 'a' to find the focus and directrix. In this case, 4a = 8 , so 'a' = 2.
03

Find the Focus

The focus of a parabola that opens to the right is given by \((h+a, k)\). Substituting h = 0 and a = 2, the Focus = (2, 0).
04

Determine the Directrix

The equation for a vertical directrix to the right opening parabola is \(x = h - a\). Substituting h = 0 and a = 2, we get the directrix as \(x = -2\).

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