Answer:
(a) [tex](x+2)^2+(y-3)^2=6^2[/tex]
(b) [tex](x-5)^2+(y+7)^2=2^2[/tex]
Step-by-step explanation:
The standard form of circle is
[tex](x-a)^2+(y-b)^2=r^2[/tex]
where, (a,b) is center and r is radius.
Properties of algebra:
[tex](a+b)^2=a^2+2ab+b^2[/tex]
[tex](a-b)^2=a^2-2ab+b^2[/tex]
(a)
Consider the given equation is
[tex]x^2+4x+4+y^2-6y+9=36[/tex]
[tex](x^2+4x+4)+(y^2-6y+9)=36[/tex]
[tex](x^2+2x(2)+2^2)+(y^2-2y(3)+3^3)=6^2[/tex]
Using properties of algebra, we get
[tex](x+2)^2+(y-3)^2=6^2[/tex]
(b)
Consider the given equation is
[tex]x^2-10x+25+y^2+14y+49=4[/tex]
[tex](x^2-10x+25)+(y^2+14y+49)=4[/tex]
[tex](x^2-2x(5)+5^2)+(y^2+2y(7)+7^2)=2^2[/tex]
Using properties of algebra, we get
[tex](x-5)^2+(y+7)^2=2^2[/tex]
