Question

Which rectangular equation is equivalent to the polar equation rcsc 9 = 8? O A x²+(y - 4² - 16 = B. x= 8y2 O C. y = 8 D. X = 8 SULTAT PREVIOUS

Answer 1

we have the equation

rcsc(theta)=8

Remember that

csc(theta)=1/sin(theta)

substitute

r(1/sin(theta))=8

r=8sin(theta)

Multiply both sides by r

r^2=8rsin(theta)

Remember that

y=rsin(theta)

so

r^2=8y

and

x^2+y^2=r^2

therefore

x^2+y^2=8y

Group terms

x^2+(y^2-8y)=0

complete the square

x^2+(y-4)^2=16

the answer is option A