Question

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

Answer 1

b on edge

Explanation:

Answer 2

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

Explanation:

The given equation is;

`r=(-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=√(x^2+y^2)`

`2√(x^2+y^2)=-12-y`

Square both sides;

`(2√(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`