x= r cos `theta`
y = r sin `theta`
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:
Now we use the above relationships `x^(2)+y^(2)=r^(2) ` and `y = r sintheta ` to rewrite the equation as follows:
It is the equation of a circle.
the equation `x^2+y^2-5y=0` can also be written as:
So it is the equation of a circle with center(0,5/2) and the radius 5/2 or 2.5units.
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