Question

Cartesian form of polar equation r=8/{6cos θ + sin θ}

Answer 1

x2 + (y − 4)2 = 16

Explanation:

edge certified 2020

Answer 2

The cartesian form of the polar equation is:
`y=-6x+8`

Explanation:

Start by multiplying both sides of the equal sign by the denominator on the right, so we get rid of all denominators:

`r=(8)/(6\,cos(\theta)+sin(\theta)) \\r *\,(6\,cos(\theta)+sin(\theta))=8\\6\,r\,cos(\theta)+r\,sin(\theta)=8`

Now recall the relationships for the "x" and "y" cartesian variables:

`x=r\,cos(\theta)\\y=r\,sin(\theta)`

So we use this identities to replace the polar coordinates in our equation, obtaining:

`6\,r\,co(\theta)+r\,sin(\theta)=8\\6\,x+y=8\\y=-6x+8`

Which renders a line with slope -6 and y-intercept +8