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Chapter 6: Problem 27

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. Directrix: \(x=-1\)

Short Answer

Expert verified
The standard form of the equation of the parabola is \(y^2 = 4x\).

Step by step solution

01

Determine the orientation

Since the directrix is \(x = -1\), a vertical line, the parabola will open towards the positive x-axis or right.
02

Find the value of 'a'

As the vertex is at origin and directrix at \(x= -1\), the distance 'a' from the vertex to the directrix (absolute value) will be \(a = |-1 - 0| = 1\)
03

Forming the equation

The standard form of the equation of a parabola that opens to the right is \(y^2 = 4ax\). Substitute \(a = 1\) to this, we get the equation \(y^2 = 4x\).

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Most popular questions from this chapter

Identify the conic as a circle or an ellipse. Then find the center, radius, vertices, foci, and eccentricity of the conic (if applicable), and sketch its graph. \(\frac{x^{2}}{4 / 9}+\frac{(y+1)^{2}}{4 / 9}=1\)

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Identify the conic as a circle or an ellipse. Then find the center, radius, vertices, foci, and eccentricity of the conic (if applicable), and sketch its graph. \(\frac{(x+5)^{2}}{9 / 4}+(y-1)^{2}=1\)
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