need help with polar question

Question

y=2x=3 then the answer would be

Y= ?

Answer 1

Assuming this problem is r = 28/(6sin(θ) + 25cos(θ)) then multiply both sides by "6sin(θ) + 25cos(θ)" to get:

r(6sin(θ) + 25cos(θ)) = 28 then distribute the "r" to get:

6rsin(θ) + 25rcos(θ) = 28

Now we use the conversion between polar coordinates to Cartesian coordinates which are:

x = rcos(θ)

y = rsin(θ)

Substituting "x" for "rcos(θ)" and "y" for "rsin(θ)" we get:

6y + 25x = 28

6y = -25x + 28

y = -25/6x + 28/6

y = -25/6x + 14/3

You can use Desmos to graph both equations (one in polar, and the other in Cartesian coordinates) and then look to see they are the same.

Answer 2

r (6 sin θ + 25 cos θ) = 28

r (6x / r + 25y / r) = 28

6x + 25y = 28

25y = -6x + 28

y = -6x/25 + 28/25