Pre-Calculus Question. Please Help!

Question

Convert the following Cartesian equation into a polar equation.If you need to include the symbol θ in your answer, use the word "theta" instead.

y = 4x +5

Answer 1

y=4x +5 y=r(theta), x= rcos(theta)

rsin(theta) = 4rcos(theta) + 5

rsin(theta) -4cos(theta) = 5

r[sin(theta) -4cos(theta)] = 5

r = 5/[sin(theta) - 4cos(theta)

or

x^2 + y^2 = r^2

y^2 = r^2 -x^2

y=4x +5

r^2-x^2 = (4x +5)^2

r^2 -x^2 = 16x^2 + 40x + 25

r^2 = 17x^2 + 40x + 25

r^2 = 17(rcos^2(trheta) + 40rcos(theta) + 25

main things to remember are r^2 = x^2 + y^2 and x=rcos(theta), y =rsin(theta)

then plug them into to convert to polar

Answer 2

y = 4x + 5; rsinθ = 4rcosθ + 5, r(sinθ - 4cosθ) = 5; r = 5/(sinθ - 4cosθ)