Answer :
We have been an equation in polar coordinates [tex]r=10\text{sin}(\theta)[/tex]. We are asked to write our equation in rectangular coordinates.
We know that the equation [tex]r=2b\text{sin}(\theta)[/tex] is equation of a circle with a radius [tex]|b|[/tex] and center at [tex](0,b)[/tex].
Let us find the value of b.
[tex]2b\text{sin}(\theta)=10\text{sin}(\theta)[/tex]
[tex]\frac{2b\text{sin}(\theta)}{2\text{sin}(\theta)}=\frac{10\text{sin}(\theta)}{2\text{sin}(\theta)}[/tex]
[tex]b=5[/tex]
We know that equation of a circle in rectangular coordinates is [tex](x-h)^2+(y-k)^2=r^2[/tex]
Since [tex]b=5[/tex], so radius is 5 and center is at point (0,5).
[tex](x-0)^2+(y-5)^2=5^2[/tex]
[tex]x^2+(y-5)^2=25[/tex]
Therefore, our required equation would be [tex]x^2+(y-5)^2=25[/tex].