Question

convert the polar equation to rectangular form.

1.) r sec(theta) = 3
2.) r = 4 cos(theta) - 4 sin(theta)

convert from rectangular equation to polar form.
1.) x^2 + (y-1)^2 = 1
2.) (x-1)^2 + (y+4)^2 = 17

Answer 1

1)r=3cos(theta)
r^2=3rcos(theta)
x^2+y^2=3x
2)r=4cos(theta)-4sin(theta)
r^2=4rcos(theta)-4rsin(theta)
x^2+y^2=4x-4y
x^2-4x +y^2+4y =0
x^2-4x+4+y^2+4y+4=4+4
(x-2)^2 +(y+2)^2=8

1)x^2+(y-1)^2=1
x^2+y^2-2y+1=1
x^2+y^2=2y
r^2=2rsin(theta)
r=2sin(theta)
2)(x-1)^2+(y+4)^2=17
x^2-2x+1+y^2+8y+16=17
x^2+y^2=2x-8y
r^2=2rcos(theta)-8rsin(theta)
r=2cos(theta)-8sin(theta)

Answer 2

thank you soooooooooo much