Chapter 10: Q. 34 (page 644)

Find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation by hand.
Focus at $(2, 4)$ ; directrix the line x = -4

Short Answer

Expert verified

The equation of the parabola is $3 y^{2} - 12 y - 4 x + 11 = 0$ .

Step by step solution

Step 1. Given information .

Consider the given vertex and directrix .

Step 2. Equation of parabola used.

A parabola whose focus is at $(2, 4)$ and directrix is the horizontal line x = -4 has its vertex $(- 1, 2)$ .

The equation of parabola is ${(y - k)}^{2} = 4 a (x - h)$ .

Substitute the values of focus and vertex in the equation of parabola to find a.

${(y - k)}^{2} = 4 a (x - h) {(4 - 2)}^{2} = 4 a (2 + 1) a = \frac{1}{3}$

Further simplify.

${(y - 2)}^{2} = \frac{4}{3} (x + 1)$

Step 3. Plot the graph.

The graph of the given equation shown below .

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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.
Focus at $(2, 4)$ ; directrix the line x = -4

Short Answer

Step by step solution

Step 1. Given information .

Step 2. Equation of parabola used.

Step 3. Plot the graph.

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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.Focus at 2,4; directrix the line x = -4

Short Answer

Step by step solution

Step 1. Given information .

Step 2. Equation of parabola used.

Step 3. Plot the graph.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Theoretical and Mathematical Physics

Statistics

Decision Maths

Mechanics Maths

Discrete Mathematics

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.
Focus at $(2, 4)$ ; directrix the line x = -4