Question

Transform the following polar equation into an equation in rectangular coordinates:
r = -4 sin theta

Answer 1

Out of the four options:
A. x=-4y
B. x+y=-4
C. y=-4
D. x^2+(y+2)^2=4
D is the correct answer

Answer 2

The equation r = - 4 sinθ, can be written in rectangular coordinates as -

$x^{2} +y^{2} =-4y$

We have a equation in polar coordinates -

r = - 4 sin θ

We have to convert it into rectangular coordinates (x, y).

What is the relation between Polar - coordinates and Rectangular - Coordinates?

The following relation exists between the polar and rectangular coordinates -

$r=\sqrt{x^{2} +y^{2} }$                 (Eqn. 1)

x = r cosθ                      (Eqn. 2)

y = r sinθ                       (Eqn. 3)

                                                               

(You can refer to image attached for conceptual clearance)

Now, we have -

r = - 4 sinθ

Multiply by ' r '  on both sides of equation, we get -

$r^{2} = 4r\;sin$  θ

We know :

                                            $r=\sqrt{x^{2} +y^{2} }$                             (from Eqn. 1)

                                            y = r sinθ                                    (from Eqn. 3)

Substituting the values, we get -

                                            $x^{2} +y^{2} =-4y$

                                                     

Hence, the equation r = - 4 sinθ, can be written in rectangular coordinates as -

                                           $x^{2} +y^{2} =-4y$

To solve more questions on transforming equation from polar form to rectangular form, visit the link below -

brainly.com/question/2293027

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