x= r cos `theta`

y = r sin `theta`

x^(2)+y^(2)=r^(2)

use above data to rewrite the expression in rectangular form, also need help to identify the equation as that of a line, circle,vertial parabola, or horizontal parabola.

r= 5 sin theta

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`x= r costheta `

`y = r sintheta `

`x^(2)+y^(2)=r^(2) ` (given)

To rewrite the expression in rectangular form

First multiply both sides by r. We get:

`r^2=5rsin theta`

Now we use the above relationships `x^(2)+y^(2)=r^(2) ` and `y = r sintheta ` to rewrite the equation as follows:

`x^(2)+y^(2)=5y`

`rArr x^(2)+y^(2)-5y=0`

**It is the equation of a circle.**

the equation `x^2+y^2-5y=0` can also be written as:

`(x-0)^2+(y-5/2)^2=(5/2)^2`

**So it is the equation of a circle with center(0,5/2) and the radius 5/2 or 2.5units.**

**Sources:**

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