Question

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

Answer 1

Answer:

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

Step-by-step explanation:

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

$r=\frac{8}{6\,cos(\theta)+sin(\theta)} \\r *\,(6\,cos(\theta)+sin(\theta))=8\\6\,r\,cos(\theta)+r\,sin(\theta)=8$

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