Rewrite the cartesian equation y = 5x^{2} as a polar equation.

a2linetagadaW

a2linetagadaW

Answered question

2021-09-12

Rewrite the cartesian equation y=5x2 as a polar equation.
r(θ) = ?

Answer & Explanation

okomgcae

okomgcae

Skilled2021-09-13Added 93 answers

Step 1
Concept: In polar coordinates,

x=rcosθ,y=rsinθ and x2+y2=r2

Here, the objective is to express the cartesian equation into polar equation.

Step 2

Substitute rsinθ for y and rcosθ​​​​​​​ to x into equation y=5x2and simplify as,

rsin0=5(rcos0)2

rsin0=5r2cos20

5r2cos20rsin0=0

r(5rcos20sin0)=0

5rcos20sin0=0

5rcos20=sin0

r=sin05cos20

r=15sin0sec20

Therefore, the polar equation is r(0)=15sin0sec20

Jeffrey Jordon

Jeffrey Jordon

Expert2021-11-27Added 2605 answers

Answer is given below (on video)

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