Answer and explation

Question

y=2x

2

−4+4

Rewrite the equation

Rewrite in polar form

​

r=0

r=

1+cos(2θ)

sin(θ)

​

​

Evaluate

y=2x

2

−4+4

Add the terms

y=2x

2

Move the expression to the left side

y−2x

2

=0

To convert the equation to polar coordinates,substitute x for r×cos(θ) and y for r×sin(θ)

sin(θ)r−2(cos(θ)r)

2

=0

Factor the expression

−2cos

2

(θ)r

2

+sin(θ)r=0

Simplify the expression

(−1−cos(2θ))r

2

+sin(θ)r=0

Factor the expression

r((−1−cos(2θ))r+sin(θ))=0

When the product of factors equals 0,at least one factor is 0

​

r=0

(−1−cos(2θ))r+sin(θ)=0

​

Solution

​

r=0

r=

1+cos(2θ)

sin(θ)

​

​

Function

Find the vertex

(0,0)

Testing for symmetry

Testing for symmetry about the origin

Not symmetry with respect to the origin

Identify the conic

Write the equation in standard form

x

2

=

2

1

​

y