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

emancipezN

emancipezN

Answered question

2021-09-26

Find a polar equation for the curve represented by the given Cartesian equation.
x2+y2=6x4y

Answer & Explanation

smallq9

smallq9

Skilled2021-09-27Added 106 answers

Step 1
Given equation is : x2+y2=6x4y
Concept : To convert an equation in polar form, we substitue x=rcosθ and y=rsinθ ;  where r = length of the pole and θ is the angle of the pole with +x axis
Now, we know 
x=rcosθ
y=rsinθ
Step 2
x2+y2=6x4y
(rcosθ)2+(rsinθ)2=6rcosθ4rsinθ
r2cos2θ+r2sin2θ=6rcosθ4rsinθ
r2(cos2θ+sin2θ)=6rcosθ4rsinθ
r2=r(6cos04sin0)   [cos20+sin20=1]

r=6cos04sin0   (cancelling out r from both side)
r=6cos04sin0

Jeffrey Jordon

Jeffrey Jordon

Expert2021-11-27Added 2605 answers

Answer is given below (on video)

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