SOLUTION: Write each cartesian equation in polar form a) x^2 + y^2 = 16 b) x^2 + y^2 = 10 c) y = 3 d) y = -4x e) 3xy = 5

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Write each cartesian equation in polar form a) x^2 + y^2 = 16 b) x^2 + y^2 = 10 c) y = 3 d) y = -4x e) 3xy = 5      Log On


   

Question 1157773: Write each cartesian equation in polar form
a) x^2 + y^2 = 16
b) x^2 + y^2 = 10
c) y = 3
d) y = -4x
e) 3xy = 5
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
a)
x%5E2+%2B+y%5E2+=+16
to convert to Polar apply: x=r%2Acos+%28theta+%29,y=r%2Asin%28theta+%29
%28r%2Acos+%28theta+%29%29%5E2+%2B+%28r%2Asin%28theta+%29%29%5E2+=+16
r%5E2%2Acos%5E2+%28theta+%29+%2B+r%5E2%2Asin%5E2%28theta+%29+=+16
r%5E2%28cos%5E2+%28theta+%29+%2B+sin%5E2%28theta+%29%29+=+16
r%5E2%281%29+=+16
So, in your case, the equation becomes simply
r%5E2+=+16
This means that the equation represents all the points with distance+4 from the origin, which is a circumference with radius 4, centered in the origin.

b)
x%5E2+%2B+y%5E2+=+10
x=r%2Acos+%28theta+%29,y=r%2Asin%28theta+%29
%28r%2Acos+%28theta+%29%29%5E2+%2B+%28r%2Asin%28theta+%29%29%5E2+=+10
r%5E2%28cos%5E2+%28theta+%29+%2B+sin%5E2%28theta+%29%29+=+10
r%5E2%281%29+=+10
the equation becomes simply
r%5E2+=+10

c)
y+=+3
y=r%2Asin%28theta+%29
r%2Asin%28theta+%29=3


d)
y+=+-4x
r%2Asin%28theta+%29=-4r%2Acos+%28theta+%29
r%2Asin%28theta+%29%2B4r%2Acos+%28theta+%29=0
r%28sin%28theta%29+%2B+4cos%28theta%29%29+=+0

e)
3xy+=+5
3r%2Acos+%28theta+%29%2Ar%2Asin%28theta+%29=5
3r%5E2%2Acos+%28theta+%29%2Asin%28theta+%29=5