Answer:
The cartesian form of the polar equation is: [tex]y=-6x+8[/tex]
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:
[tex]r=\frac{8}{6\,cos(\theta)+sin(\theta)} \\r *\,(6\,cos(\theta)+sin(\theta))=8\\6\,r\,cos(\theta)+r\,sin(\theta)=8[/tex]
Now recall the relationships for the "x" and "y" cartesian variables:
[tex]x=r\,cos(\theta)\\y=r\,sin(\theta)[/tex]
So we use this identities to replace the polar coordinates in our equation, obtaining:
[tex]6\,r\,co(\theta)+r\,sin(\theta)=8\\6\,x+y=8\\y=-6x+8[/tex]
Which renders a line with slope -6 and y-intercept +8
Answer:
x2 + (y − 4)2 = 16
Step-by-step explanation:
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