Question

Convert the polar equation to an equivalent rectangular equation:

Answer 1

Answer:

The correct answer will be option b

Step-by-step explanation:

We know that x = rcos( θ ), and y = rsin( θ ), so let's rewrite this polar equation.

r = 4( x / r ) + 2( y / r ),

r = 4x / r + 2y / r,

r = 4x + 2y / r,

r / 1 = 4x + 2y / r ( Cross - Multiply )

4x + 2y = r²

We also know that r² = x² + y², so let's substitute.

x² + y² = 4x + 2y,

x² - 4x - 2y + y² = 0,

Circle Equation : ( x - 2 )² + ( y - 1 )² = ( √5 )²,

Solution : ( x - 2 )² + ( y - 1 )² = 5