Question

HELP
What is the name of the shape graphed by the function R^2 = 4cose theta?
A. Circle
B. Lemniscate
C. Limaçon with inner loop
O D. Line

Answer 1

Answer:

Hence, r=2cosθ represents a circle with centre (1,0) and radius 1 and (1,0) in polar coordinates too is (1,0

Step-by-step explanation:

hope this helps;)

Answer 2

The name of the shape graphed by the function $r^{2} = 4\;cos$ θ is Limaçon with inner loop.

We have the following function -

$r^{2} = 4\;cos$ θ

We have to find the shape represented by this function.

What are Polar Coordinates?

Polar coordinates are used to represent a point in a two - dimensional plane. In polar coordinate system, the point under consideration is represented with the help of two variables namely $r$ and θ. (Take the reference from the figure attached)

We have -

$r^{2} = 4\;cos$ θ

The relation between variables in polar coordinates and cartesian coordinates is -

$x = rcos\theta\\y=rsin\theta\\r=\sqrt{x^{2} +y^{2} }$

First, lets convert this equation in the rectangular coordinates -                                                      

$r^{3} =4\;r\;cos\;\theta\\r\times\;r^{2} = 4\;r\;cos\;\theta\\\sqrt{x^{2} +y^{2} }\;\times\;(x^{2} +y^{2}) = 4x\\(x^{2} +y^{2})=\frac{4x}{\sqrt{x^{2} +y^{2} }}$

The above equation in rectangular coordinate system represents a Limaçon with inner loop.

Hence, the name of the shape graphed by the function $r^{2} = 4\;cos$ θ is

Limaçon with inner loop.

To solve more questions on identifying the shape of the graph by the function, visit the link below -

https://brainly.com/question/9422589

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