Chapter 9: Q. 70 (page 568)

The letters x and y represent rectangular coordinates. Write each equation using polar coordinates $(r, θ)$ .
$y^{2} = 2 x$

Short Answer

Expert verified

The equation using polar coordinates is $r^{2} \sin^{2} θ - 2 r \cos θ = 0$ .

Step by step solution

Step 1. Given Information and Concept used

We are given an equation,

$y^{2} = 2 x$

If P is a point with polar coordinates $(r, θ)$ , the rectangular coordinates $(x, y)$ of P are given by,

$x = r \cos θ y = r \sin θ$

Step 2. Converting into polar coordinates

Substituting the value of x and y,we get

$(r \sin θ)^{2} = 2 (r \cos θ) r^{2} \sin^{2} θ = 2 r \cos θ r^{2} \sin^{2} θ - 2 r \cos θ = 0$

The equation is $r^{2} \sin^{2} θ - 2 r \cos θ = 0$ .

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The letters x and y represent rectangular coordinates. Write each equation using polar coordinates $(r, θ)$ .
$y^{2} = 2 x$

Short Answer

Step by step solution

Step 1. Given Information and Concept used

Step 2. Converting into polar coordinates

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The letters x and y represent rectangular coordinates. Write each equation using polar coordinates r,θ. y2=2x

Short Answer

Step by step solution

Step 1. Given Information and Concept used

Step 2. Converting into polar coordinates

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Decision Maths

Calculus

Theoretical and Mathematical Physics

Pure Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

The letters x and y represent rectangular coordinates. Write each equation using polar coordinates $(r, θ)$ .
$y^{2} = 2 x$