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Chapter 6: Problem 55

Find the standard form of the equation of the parabola with the given characteristics. Vertex: (4,3)\(;\) focus: (6,3)

Short Answer

Expert verified
The provided exercise appears to have an error since it leads to division by zero. The focus and the vertex of a parabola cannot have the same coordinates.

Step by step solution

01

Determine the direction of the parabola

First, evaluate the alignment of the vertex and the focus of the parabola. Here, the vertex is given as (4,3) and the focus is given as (6,3). Both points share the same y-coordinate, which means the parabola opens horizontally.
02

Insert the given vertex into the corresponding standard form

Since the parabola opens horizontally, the standard form should be \(x = a(y-k)^2 + h\), where (h,k) is the vertex. Inserting the vertex, we get \(x = a(y-3)^2 + 4\).
03

Determine 'a' using the focus

The formula that links the focus, vertex and 'a' in a parabola that opens horizontally is \(h = a(k-p)^2 + f\), where (f,p) are the coordinates of the focus. This can be rearranged to find 'a': \(a = (h-f) / (k-p)^2\). Inserting the coordinates given for the focus (6,3) along with the vertex (4,3), we have \(a = (4-6) / (3-3)^2\), which simplifies to \(a = -2 / 0\). However, division by zero is undefined, indicating there may be a mistake in the provided exercise.

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Most popular questions from this chapter

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