Find a polar equation for the curve represented by the given Cartesian equation.

OlmekinjP

OlmekinjP

Answered question

2021-09-20

Find a polar equation for the curve represented by the given Cartesian equation. y = 1 + 3x

Answer & Explanation

okomgcae

okomgcae

Skilled2021-09-21Added 93 answers

y=1+3x
To find the polar equation, we will replace x with rcosθ and y with rsinθ in the above equation
rsinθ=1+3rcosθ
Subtract 3rcosθ from both sides
rsinθ3rcosθ=1
Take out r as the common factor in the left-hand side
r(sinθ3cosθ)=1
Divide both sides by sinθ3cosθ (this is allowed because it is non-zero, the above equation is not true when it happens to be 0)
r=1sinθ3cosθ
This is the polar equation we were looking for
Result: r=1sinθ3cosθ

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