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Chapter 7: Problem 58

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 \(y^2 = 8x\) is at the point (2, 0) and the directrix is at \(x = -2\).

Step by step solution

01

Identify the value of 'a'

The equation of the parabola is given as \(y^2 = 8x\). This equation is in the form of \(y^2 = 4ax\). Comparing the two, it is clear that 4a = 8. We can solve for 'a' by dividing 8 by 4. Therefore, \(a = 2\).
02

Find the Focus

The focus of the parabola in this form is at the point \((a, 0)\). We have calculated 'a' as 2, so the focus is at the point \((2, 0)\).
03

Find the Directrix

The equation of the directrix for a parabola in this form is \(x = -a\). With 'a' calculated as 2, this gives the equation of the directrix as \(x = -2\).

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