To identify the graph of the function, we first need to convert the equation from polar to Cartesian coordinates.

The conversion formulas are:
x = r cos θ
y = r sin θ

Given the equation r = -2 cos θ - 4 sin θ, we multiply both sides by r to get:
r^2 = -2r cos θ - 4r sin θ

Substituting the conversion formulas into the equation, we get:
x^2 + y^2 = -2x - 4y

Rearranging the terms, we get:
x^2 + 2x + y^2 + 4y = 0

To complete the square, we add and subtract (2/2)^2 = 1 on the left side and add and subtract (4/2)^2 = 4 on the right side to get:
(x + 1)^2 + (y + 2)^2 = 1^2 + 2^2

Simplifying, we get:
(x + 1)^2 + (y + 2)^2 = 5

This is the equation of a circle with center at (-1, -2) and radius sqrt(5). So, the answer is (a) Circle.

Question

To identify the graph of the function, we first need to convert the equation from polar to Cartesian coordinates.

The conversion formulas are: 
x = r cos θ 
y = r sin θ

Given the equation r = -2 cos θ - 4 sin θ, we multiply both sides by r to get: 
r^2 = -2r cos θ - 4r sin θ

Substituting the conversion formulas into the equation, we get: 
x^2 + y^2 = -2x - 4y

Rearranging the terms, we get: 
x^2 + 2x + y^2 + 4y = 0

To complete the square, we add and subtract (2/2)^2 = 1 on the left side and add and subtract (4/2)^2 = 4 on the right side to get: 
(x + 1)^2 + (y + 2)^2 = 1^2 + 2^2

Simplifying, we get: 
(x + 1)^2 + (y + 2)^2 = 5

This is the equation of a circle with center at (-1, -2) and radius sqrt(5). So, the answer is (a) Circle.

Knowee AI · Accepted Answer

To identify the graph of the function, we first need to convert the equation from polar to Cartesian coordinates.

The conversion formulas are: 
x = r cos θ 
y = r sin θ

Given the equation r = -2 cos θ - 4 sin θ, we multiply both sides by r to get: 
r^2 = -2r cos θ - 4r sin θ

Substituting the conversion formulas into the equation, we get: 
x^2 + y^2 = -2x - 4y

Rearranging the terms, we get: 
x^2 + 2x + y^2 + 4y = 0

To complete the square, we add and subtract (2/2)^2 = 1 on the left side and add and subtract (4/2)^2 = 4 on the right side to get: 
(x + 1)^2 + (y + 2)^2 = 1^2 + 2^2

Simplifying, we get: 
(x + 1)^2 + (y + 2)^2 = 5

This is the equation of a circle with center at (-1, -2) and radius sqrt(5). So, the answer is (a) Circle.

A graph in polar coordinates is of the form: r = -2 cos⁡θ - 4 sin⁡θ. Identify the graph of this function. Hint: Multiply both sides by r and then convert to Cartesian form. a. Circle b. Ellipse c. Hyperbola d. Line e. Parabola

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