Question

Q1: Convert r =-72/12+6 sin theta to Cartesian form. (Picture Provided Below)

Answer 1

Answer:

b. $4x^2+3y^2-24y-144=0$

Step-by-step explanation:

The given equation is;

$r=\frac{-72}{12+6\sin(\theta)}$

Cross multiply;

$r(12+6\sin(\theta)=-72$

Expand;

$12r+6r\sin(\theta)=-72$

Divide through by 6;

$2r+r\sin(\theta)=-12$

$2r=-12-r\sin(\theta)$

Substitute;

$y=r\sin(\theta), r=\sqrt{x^2+y^2}$

$2\sqrt{x^2+y^2}=-12-y$

Square both sides;

$(2\sqrt{x^2+y^2})^2=(-12-y)^2$

$4(x^2+y^2)=144+24y+y^2$

$4x^2+4y^2=144+24y+y^2$

Simplify;

$4x^2+3y^2-24y-144=0$