Which rectangular equation is equivalent to the polar equation r csc theta=8?

Rectangular and polar forms are two forms of equations that translates to plot. In this case, the two forms are convertible to each other by the expressions:

r sin theta = y

r cos theta = x

x2 + y2 = r2

we are given the polar expression r csc theta = 8 and is asked to convert to rectangular form.

in this case, csc theta is equal to 1 / sin theta. thys

r / sin theta = 8

in order to make use of the equations above, then

we multiply r to both numerator and denominator in the left side, that is

r^2 / r sin theta = 8

x2+y2 / y = 8

x 2 + y2 = 8y