Question

X^2+y^2-4x-3y in polar form

Answer 1

x^2+y^2-4x-3y in polar form is r = 4r cos θ +  3r sin θ

How to convert to polar form

The conversion from rectangular to polar form is given by;

x = r cos θ

y = r sin θ

Given the expression as;

x² + y² -4x-3y

x² + y² = 4x + 3y

Now, substitute the values, we have

(r cos θ)² +( r sin θ)² = 4 ( r cos θ) + 3 ( r sin θ)

r² cos²θ + r² sin² θ = 4r cos θ +  3r sin θ

Factor out the r²

r² ( cos² θ + sin² θ) = 4r cos θ +  3r sin θ

Apply Pythagorean identity:

cos² θ + sin² θ = 1

Substitute into the expression

r²  ( 1) = 4r cos θ +  3r sin θ

Set the expression equal to 0:

r² - 4r cos θ -  3r sin θ = 0

Factor out the r:

r ( r - 4 cos θ - 3 sin θ ) = 0

r = 0

r = 4r cos θ +  3r sin θ

Thus, x^2+y^2-4x-3y in polar form is r = 4r cos θ +  3r sin θ

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