Question

3123
Which of the following is rectangular equation of the polar equation; r = 4coso+8sino
О 99972 = 4x+8y
0 (0–2)2+(y-4)2 = 20
O2+42 = 20
(30–4)2+(y-2)2 = 20​

Answer 1

Given :  polar Equation r = 4 cosθ  + 8 Sinθ  

To find : rectangular equation

Solution:

r = 4 cosθ  + 8 Sinθ  

x = r cosθ  => cosθ = x/r

y = r sinθ => Sinθ = y/r

x² + y² = r²

r = 4 cosθ  + 8 Sinθ  

=> r = 4 (x/r)  + 8(y/r)

=> r² = 4x  + 8y

=> x² + y² = 4x + 8y

=> x² - 4x  + y² - 8y = 0

=> (x - 2)² - 4 + (y - 4)² - 16 = 0

=> (x - 2)²  + (y - 4)²   = 20

(x - 2)²  + (y - 4)²   = 20  is the  rectangular equation of the polar equation r = 4 cosθ  + 8 Sinθ

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