Question

a curve with polar equation represents a line. this line has a cartesian equation of the form ,where and are constants. give the formula for in terms of . for example, if the line had equation then the answer would be . y

Answer 1

Solution:
r = 43 /(3sin(t) + 19cos(t))

Formulas:
x = r*cos(t)
y = r*sin(t)
r^2 = x^2 + y^2

cos(t) = x/r
sin(t) = y/r

Substitute into the equation to get:
r = 43 /(3sin(t) + 19cos(t))
r = 43 /(3(y/r) + 19(x/r))
r = [43*r] /[3y + 19x]

Divide both sides by r to get:
1 = 43 /[3y + 19x]
3y + 19x = 43
3y = -19x + 43
y = -(19/3)x + 43/3

THEREFORE
-(19/3)x + 43/3

Hope this helps have an excellent day!