<h2>
Answer with explanation:</h2>
We know that the standard form of a circle is given by the equation:
![(x-h)^2+(y-k)^2=r^2](https://tex.z-dn.net/?f=%28x-h%29%5E2%2B%28y-k%29%5E2%3Dr%5E2)
where the center if the circle is at (h,k) and the radius of circle is: r
1)
![x^2+y^2-2x+2y-1=0](https://tex.z-dn.net/?f=x%5E2%2By%5E2-2x%2B2y-1%3D0)
on converting to standard form of equation we get:
![(x-1)^2+(y+1)^2=(\sqrt{3})^2](https://tex.z-dn.net/?f=%28x-1%29%5E2%2B%28y%2B1%29%5E2%3D%28%5Csqrt%7B3%7D%29%5E2)
Hence, the radius of circle is:√3=1.732 units
2)
![x^2+y^2-4x+4y-10=0](https://tex.z-dn.net/?f=x%5E2%2By%5E2-4x%2B4y-10%3D0)
on converting to standard form of equation we get:
![(x-2)^2+(y+2)^2=(\sqrt{18})^2](https://tex.z-dn.net/?f=%28x-2%29%5E2%2B%28y%2B2%29%5E2%3D%28%5Csqrt%7B18%7D%29%5E2)
Hence, the radius of circle is:3√2=4.242 units
3)
![x^2+y^2-8x-6y-20=0](https://tex.z-dn.net/?f=x%5E2%2By%5E2-8x-6y-20%3D0)
on converting to standard form of equation we get:
![(x-4)^2+(y-3)^2=(\sqrt{45})^2](https://tex.z-dn.net/?f=%28x-4%29%5E2%2B%28y-3%29%5E2%3D%28%5Csqrt%7B45%7D%29%5E2)
Hence, the radius of circle is:3√5=6.708 units
4)
![4x^2+4y^2+16x+24y-40=0](https://tex.z-dn.net/?f=4x%5E2%2B4y%5E2%2B16x%2B24y-40%3D0)
on dividing both side by 4 we get:
![x^2+y^2+4x+6y-10=0](https://tex.z-dn.net/?f=x%5E2%2By%5E2%2B4x%2B6y-10%3D0)
on converting to standard form of equation we get:
![(x+2)^2+(y+3)^2=(\sqrt{23})^2](https://tex.z-dn.net/?f=%28x%2B2%29%5E2%2B%28y%2B3%29%5E2%3D%28%5Csqrt%7B23%7D%29%5E2)
Hence, the radius of circle is:
=4.796 units
5)
![5x^2+5y^2-20x+30y+40=0](https://tex.z-dn.net/?f=5x%5E2%2B5y%5E2-20x%2B30y%2B40%3D0)
on dividing both side by 5 we get:
![x^2+y^2-4x+6y+8=0](https://tex.z-dn.net/?f=x%5E2%2By%5E2-4x%2B6y%2B8%3D0)
on converting to standard form of equation we get:
![(x-2)^2+(y+3)^2=(\sqrt{5})^2](https://tex.z-dn.net/?f=%28x-2%29%5E2%2B%28y%2B3%29%5E2%3D%28%5Csqrt%7B5%7D%29%5E2)
Hence, the radius of circle is:√5=2.236 units
6)
![2x^2+2y^2-28x-32y-8 = 0](https://tex.z-dn.net/?f=2x%5E2%2B2y%5E2-28x-32y-8%20%3D%200)
on dividing both side by 2 we get:
![x^2+y^2-14x+16y-4=0](https://tex.z-dn.net/?f=x%5E2%2By%5E2-14x%2B16y-4%3D0)
on converting to standard form of equation we get:
![(x-7)^2+(y+8)^2=(\sqrt{117})^2](https://tex.z-dn.net/?f=%28x-7%29%5E2%2B%28y%2B8%29%5E2%3D%28%5Csqrt%7B117%7D%29%5E2)
Hence, the radius of circle is:√117=10.817 units
7)
![x^2+y^2+12x-2y-9=0](https://tex.z-dn.net/?f=x%5E2%2By%5E2%2B12x-2y-9%3D0)
on converting to standard form of equation we get:
![(x+6)^2+(y-1)^2=(\sqrt46})^2](https://tex.z-dn.net/?f=%28x%2B6%29%5E2%2B%28y-1%29%5E2%3D%28%5Csqrt46%7D%29%5E2)
Hence, the radius of circle is:√46=6.782 units
On arranging the circle in ascending order of their radius is:
1) → 5) → 2) → 4) → 3) → 7) → 6)