Chapter 10: Q 30. (page 643)

Find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation by hand.
Vertex is at $(4, - 2)$ and focus is at $(6, - 2)$ .

Short Answer

Expert verified

The equation of a parabola is

${(y + 2)}^{2} = 8 (x - 4)$ .

The points are $(6, 2); (6, - 6)$ .

The graph of an equation is

Step by step solution

Step 1. Given Information.

The given vertex is at $(4, - 2)$ and focus is at $(6, - 2)$ .

Step 2. Equation of a parabola.

The vertex is at $(4, - 2)$ and focus $(6, - 2)$ both lie on the horizontal line $y = - 2$ (the axis of symmetry). The distance a from the vertex to the focus is $a = - 2$ .

The parabola opens to the right. The form of a equation is

${(y - k)}^{2} = - 4 a (x - h)$ .

where $(h, k) = (4, - 2)$ and $a = - 2$ . Therefore, the equation is

${(y + 2)}^{2} = 8 (x - 4)$ .

Step 3. Latus rectum.

The two points that determines the latus rectum by letting $x = 6$ , so that

${(y + 2)}^{2} = 8 (x - 4) {(y + 2)}^{2} = 8 (2) {(y + 2)}^{2} = 16 y + 2 = \pm 4 y + 2 = 4, y + 2 = - 4 y = 2, - 6 .$

The points are $(6, 2)$ and $(6, - 6)$ .

Step 4. Graphing Utility.

The graph of a parabola is

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Find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation by hand.
Vertex is at $(4, - 2)$ and focus is at $(6, - 2)$ .

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Equation of a parabola.

Step 3. Latus rectum.

Step 4. Graphing Utility.

One App. One Place for Learning.

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Find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation by hand.Vertex is at4,-2and focus is at6,-2.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Equation of a parabola.

Step 3. Latus rectum.

Step 4. Graphing Utility.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Applied Mathematics

Pure Maths

Calculus

Theoretical and Mathematical Physics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation by hand.
Vertex is at $(4, - 2)$ and focus is at $(6, - 2)$ .