Chapter 9: Q. 8 (page 631)

In Problems 8 and 9, test the polar equation for symmetry with respect to the pole, the polar axis, and the line $θ = \frac{π}{2}$ .
$r^{2} \cos θ = 5$

Short Answer

Expert verified

The polar equation is symmetric about the polar axis, the pole and the line $θ = \frac{π}{2}$ .

Step by step solution

Step 1. Given information

We are given a polar equation,

$r^{2} \cos θ = 5$

We have to check the polar equation for symmetry with respect to the pole, the polar axis, and the line $θ = \frac{π}{2}$ .

Step 2. Checking the symmetry about polar axis

We have to replace $θ$ with $- θ$ to check the symmetry,

localid="1647058749450" $r^{2} \cos (θ) = 5 r^{2} \cos (- θ) = 5$

We know that cosine function is even function, so

$r^{2} \cos (θ) = 5$

Hence, the function is symmetric about polar axis.

Step 3. Checking the symmetry about pole

We have to replace r with $- r$ to check the symmetry,

$r^{2} \cos (θ) = 5 {(- r)}^{2} \cos (θ) = 5 r^{2} \cos (θ) = 5$

Hence, the function is symmetric about the pole.

Step 4. Checking the symmetry about the line θ=π2

Since the function is symmetric about both polar axis and origin, it has to be symmetric about the line $θ = \frac{π}{2}$

Hence, the given polar equation is symmetric about the polar axis, the pole and the line $θ = \frac{π}{2}$ .

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In Problems 8 and 9, test the polar equation for symmetry with respect to the pole, the polar axis, and the line $θ = \frac{π}{2}$ .
$r^{2} \cos θ = 5$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Checking the symmetry about polar axis

Step 3. Checking the symmetry about pole

Step 4. Checking the symmetry about the line θ=π2

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In Problems 8 and 9, test the polar equation for symmetry with respect to the pole, the polar axis, and the line θ=π2.r2cosθ=5

Short Answer

Step by step solution

Step 1. Given information

Step 2. Checking the symmetry about polar axis

Step 3. Checking the symmetry about pole

Step 4. Checking the symmetry about the line θ=π2

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Pure Maths

Decision Maths

Applied Mathematics

Mechanics Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In Problems 8 and 9, test the polar equation for symmetry with respect to the pole, the polar axis, and the line $θ = \frac{π}{2}$ .
$r^{2} \cos θ = 5$