# Converting Rectangular Equation to Polar Form## Problem Statement:Convert the rectangular equation to polar form and sketch its graph.## Equation Given:\[ y^2 = 4x \]### Graphs of Possible Polar Representations:#### Graph Descriptions:1. **Graph (Top Left)**: - This graph depicts a curve opening to the right. The curve passes through the point \( (0,0) \) and extends to positive x-values.2. **Graph (Top Right)**: - This graph shows a parabolic curve opening upwards. The vertex of the parabola is at the origin \( (0,0) \), and it extends in both positive and negative directions along the x-axis.3. **Graph (Bottom Left)**: - This graph presents a curve opening to the left. The curve passes through the origin \( (0,0) \) and expands to negative x-values.4. **Graph (Bottom Right)**: - This graph illustrates another parabolic curve opening upwards, similar to the top right graph. The curve passes through the origin \( (0,0) \).### Explanation of Correct Graph:To identify which graph corresponds to the equation \( y^2 = 4x \) after converting to polar coordinates:1. The standard form for a parabola opening to the right is \( y^2 = 4ax \), indicating that it would exhibit symmetry along the y-axis and open towards the positive x-direction.2. The transformation into polar coordinates does not break this symmetry.Therefore, the correct graph for the given equation is the **Top Left Graph**.### Answer Key:- The blue circle (o) next to the top left graph indicates this graph is the correct portrayal for the given equation.

Solution:Given rectangular equation: we have to convert the given rectangular equation to polar form…

Answered: Convert the rectangular equation to…

Convert the rectangular equation to polar form and sketch its graph. y² = 4x -4 -4 -2 -2 π/2 4 2 -2 π/2 4 2 -2 2 2 4 4 0 0 -4 -4 -2 -2 π/2 4 2 -2 π/2 4 2 2 2 4 4 0 0

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: N(-3, 3*) 3. Find the equation of the line in polar coordinates that passes and the pole.

Q: 13πt Match the point in polar coordinates 3, 4 04(3, 1) 3π 4 C(3, -t) D(-3, =) OB 3, OD Ś to the…

A: This question can be solved using the concept of polar coordinates.

Q: Convert to polar form. Then isolate r. (a) x² +y² -9= 0 (b) x² +y = 4x %3D

A: x2+y2-9=0 On simplification, we get ⇒x2+y2=9⇒r2=9 ∵r=x2+y2⇒r2=x2+y2⇒r=3

Q: Replace the polar equation with an equivalent Cartesian equation. r² = 44r cos 0 (x-22)² + y²-0…

Q: Expressw= (-1-√2i) in polar form.

Q: 3π Plot the point whose polar coordinates are 2, 2 -5 -4 -3 -2 -1 5 4 3 2 1 -1 -2 -3 -4 V 1 2 3 5

A: The given polar coordinate point2, 3π2. We have to plot the point in the rectangular coordinate…

Q: Divide. 12v2cis () : 3V3cis (플) Drag a value into each box to correctly express the quotient in…

A: Use the formula below to solve this question.

Q: (a) r= 5 sin(0) O (1) (ii) O (ii) (b) r= 2 + 5 sin(0) O (1) (ii) (iii) (c) r = 5 cos(20) O (1) (ii)

A: Match each of the following polar equations with its graph

Q: Which of the following represents the rectangular equation x² + y²-5y-0 in a polar equation?

Q: nd the Cartesian and the polar form of 7e

Q: Convert the polar equation to rectangular form and sketch its graph. y

A: Given: θ=π6

Q: 2. Convert (-V3,) to rectangular form.

Q: 3. Find the polar form of the Cartesian equation: x² + y² = (3 + 2x)² %3D

A: Solution-

Q: Part I: Polar Points 1. Name the point (-2,7) in three other ways on −2ñ < 0 < 2ñ

A: Here, the given polar point is: -2,2π3

Q: ASolve the equation 4x +20= 0 and write the resulting solution in the polar form, rZ0.

Q: Find (V2 + i ) . Answers must be in Polar and Rectangular Form

A: The given problem is to express the given complex number in the form of polar form and rectangular…

Q: 9. Convert the following rectangular point to polar form: (-2,2√3) 10. Convert the following polar…

A: 9.Rectangular form (-2,2√3)We have to convert in polar form10. given polar form (-2,-7π/6)We have…

Q: Plot the point with the given polar coordinates. (4, -12) O O O O Sm - 7x 6 7x 6 5m 7x 6 22 7x 6 53…

A: The given coordinate is r,θ=4,-1112π That means at radius 4 we need to plot the angle which is in…

Q: 3. Evaluate LLA" (4- y2) dydx by using polar coordinates.

Q: Convert the rectangular equation to polar form. (x+3)sqaured + (y+1)squared=10 do not give answer in…

Question

# Converting Rectangular Equation to Polar Form

## Problem Statement:
Convert the rectangular equation to polar form and sketch its graph.

## Equation Given:
\[ y^2 = 4x \]

### Graphs of Possible Polar Representations:

#### Graph Descriptions:
1. **Graph (Top Left)**:
- This graph depicts a curve opening to the right. The curve passes through the point \( (0,0) \) and extends to positive x-values.

2. **Graph (Top Right)**:
- This graph shows a parabolic curve opening upwards. The vertex of the parabola is at the origin \( (0,0) \), and it extends in both positive and negative directions along the x-axis.

3. **Graph (Bottom Left)**:
- This graph presents a curve opening to the left. The curve passes through the origin \( (0,0) \) and expands to negative x-values.

4. **Graph (Bottom Right)**:
- This graph illustrates another parabolic curve opening upwards, similar to the top right graph. The curve passes through the origin \( (0,0) \).

### Explanation of Correct Graph:
To identify which graph corresponds to the equation \( y^2 = 4x \) after converting to polar coordinates:

1. The standard form for a parabola opening to the right is \( y^2 = 4ax \), indicating that it would exhibit symmetry along the y-axis and open towards the positive x-direction.
2. The transformation into polar coordinates does not break this symmetry.

Therefore, the correct graph for the given equation is the **Top Left Graph**.

### Answer Key:
- The blue circle (o) next to the top left graph indicates this graph is the correct portrayal for the given equation.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1: Given

Step 2: Concept used

Step 3: Calculation

Step 4: Graph

Solution

Step by step

Solved in 5 steps with 12 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Convert the polar equation r = 8cos 0 to a rectangular equation. O x² + (y-8)2 = 16 O(x-4)² + y² = 16 O x² + (y-8)2 = 64 O(x-4)² + y² = 64
6- 2- 3-12-11 -10 -9 -8 -7 -6 -5 32-1, -2- -3- -4- -5- -7- -8 -9- Write the parametric equation for the segment drawn. Tmin = Tmax = 2 %3D XT = %3D YT =

Recommended textbooks for you

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated