Question

Which equation will produce the graph shown?

Answer 1

The given graph is a polar plot. Among the equation given, the equation r = 2 cos( 3 theta) is the equation that can produce the graph shown. This graph is known as the “rose petal” polar plot graph. So the answer is letter C.

Answer 2

Answer:

Option: C is the correct answer.

C) $r=2\cos (3\theta)$

Step-by-step explanation:

A)

$\theta=\dfrac{2\pi}{3}$

is a equation of a straight line.

Hence, option(1) is discarded since we are given rose petals.

We know that a standard equation of a rose petal is given by:

                         $r=a\cos (n\theta)$

where n represents the number of rose petals.

B)

$r^2=9\cos (2\theta)\\\\i.e.\\r=3\sqrt{\cos(2\theta)}$

Hence it is not a standard form of a rose petal equation.

Hence, this option is also discarded.

D)

$3\cos (\theta)=2$

Since, this is a equation of a circle and not of rose petals.

hence, option: D is also discarded.

C)

$r=2\cos (3\theta)$

This equation is in standard form of a equation of a rose petal and also here n=3 i.e. there are 3 rose petals.

Also at θ=0°

$r=2\cos (3\theta)=2 \cos(0)=2$

Hence, at θ=0° we get the point is located at the second circle.

Hence, option: C is the correct answer.