Chapter 8: Q9. (page 423)

Write an equation for the parabola having focus $(3, 8)$ and directrix $y = 4$ . Then draw the graph.

Short Answer

Expert verified

The required equation of the parabola is $y = \frac{1}{8} {(x - 3)}^{2} + 6$ .

Step by step solution

Step 1. Write down the given information.

The given parabola has focus $(3, 8)$ and directrix $y = 4$ .

Step 2. Concept used.

If $P (x, y)$ be any point on parabola having focus $(f_{1}, f_{2})$ and directrix $y = a$ then:

Distance of point $P (x, y)$ from focus $(f_{1}, f_{2}) =$ Distance of point $P (x, y)$ from $(x, a)$

Step 3. Calculation.

Since the given parabola has focus $(3, 8)$ and directrix $y = 4$ . Therefore, apply the concept stated above,

Distance of point $P (x, y)$ from focus $(3, 8) =$ Distance of point $P (x, y)$ from $(x, 4)$

$\begin{matrix} \sqrt{{(x - 3)}^{2} + {(y - 8)}^{2}} = \sqrt{{(x - x)}^{2} + {(y - 4)}^{2}} \\ {(x - 3)}^{2} + {(y - 8)}^{2} = {(x - x)}^{2} + {(y - 4)}^{2} .... (Squaring) \\ {(x - 3)}^{2} = {(y - 4)}^{2} - {(y - 8)}^{2} \\ {(x - 3)}^{2} = (2 y - 12) (4) \\ {(x - 3)}^{2} = 8 y - 48 \\ y = \frac{1}{8} {(x - 3)}^{2} + 6 \end{matrix}$

Hence, $y = \frac{1}{8} {(x - 3)}^{2} + 6$ is the required equation of the parabola.

Step 4. Sketch the graph of the parabola.

The graph of the parabola $y = \frac{1}{8} {(x - 3)}^{2} + 6$ is shown below.

Step 5. Conclusion.

The required equation of the parabola is $y = \frac{1}{8} {(x - 3)}^{2} + 6$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Write an equation for the parabola having focus $(3, 8)$ and directrix $y = 4$ . Then draw the graph.

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Concept used.

Step 3. Calculation.

Step 4. Sketch the graph of the parabola.

Step 5. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Mechanics Maths

Decision Maths

Pure Maths

Probability and Statistics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Write an equation for the parabola having focus 3,8 and directrix y=4. Then draw the graph.

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Concept used.

Step 3. Calculation.

Step 4. Sketch the graph of the parabola.

Step 5. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Mechanics Maths

Decision Maths

Pure Maths

Probability and Statistics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Write an equation for the parabola having focus $(3, 8)$ and directrix $y = 4$ . Then draw the graph.