The answer is:
The general form of the circle is:
[tex]x^{2} -2x+y^{2} +4y=0[/tex]
We are given the standard form of a circle, so, to calculate the general form, we need to solve notable products.
We must remember the way to solve the notable product:
[tex](a+b)^{2}=a^{2}+2ab+b^{2} \\\\(a-b)^{2}=a^{2}-2ab+b^{2}[/tex]
So,
We are given the equation:
[tex](x-1)^{2}+(y+2)^{2}=5[/tex]
Then, solving the notable products, and adding/subtracting like terms, we have:
[tex]x^{2} -2*1x+1+y^{2}+2*2y+4=5\\x^{2} -2x+1+y^{2} +4y+4=5\\\\x^{2} -2x+y^{2} +4y+1+4-5=0\\\\x^{2} -2x+y^{2} +4y=0[/tex]
Hence, have that the general form of the circle is:
[tex]x^{2} -2x+y^{2} +4y=0[/tex]
Have a nice day!
