Convert x+2y=5 to polar form
recall:
cosØ = x/r ---> x = rcosØ
sinØ = y/r ---> y = rsinØ
x+2y=5
rcosØ + 2rsinØ = 5
confirm
https://www.wolframalpha.com/input/?i=polar+graph+rcos%CE%B8+%2B+2rsin%CE%B8+%3D+5
x = r cos θ
y = r sin θ
x + 2 y = 5
becomes
r cos θ + 2 r sin θ = 5
r ( cos θ + 2 sin θ ) = 5
r = 5 / ( cos θ + 2 sin θ )
To convert the equation x + 2y = 5 to polar form, we need to express it in terms of polar coordinates (r, θ), where r is the distance from the origin and θ is the angle from the positive x-axis.
First, let's make the substitution x = rcos(θ) and y = rsin(θ) in the original equation:
rcos(θ) + 2rsin(θ) = 5
Next, we can simplify this equation by factoring out the common factor of r:
r(cos(θ) + 2sin(θ)) = 5
Now, divide both sides of the equation by (cos(θ) + 2sin(θ)) to isolate r:
r = 5 / (cos(θ) + 2sin(θ))
This is the polar form of the equation x + 2y = 5.