Answer:
Equation of the circle is : [tex]x^{2} + 10x + y^{2} -4y -7 =0[/tex]
Step-by-step explanation:
Let us consider the image attached in the answer area.
The center O has the co-ordinates i.e. (-5,2) and the diameter given is 12 units.
We know that radius is half of diameter.
[tex]\text{Radius = }\dfrac{\text{Diameter}}{2}[/tex]
[tex]\text{Radius = }\dfrac{12}{2}\\\Rightarrow \text{Radius = 6units}[/tex]
The equation for circle given the center and radius, can be represented as:
[tex](x-a)^{2}+ (y-b)^{2} = r^{2}[/tex]
Where (a,b) is the co-ordinate of center and r is the radius.
Let us consider the following formula:
[tex](p+q)^2 = p^{2}+ q^{2} +2pq\\(p-q)^2 = p^{2}+ q^{2} -2pq[/tex]
[tex](x-(-5))^{2}+ (y-2)^{2} = 6^{2}\\\Rightarrow (x+5)^{2}+ (y-2)^{2} = 36\\\Rightarrow x^{2} + 25 + 10x +y^{2} + 4-4y=36\\\Rightarrow x^{2} + 10x +y^{2} -4y-7=0[/tex]
Hence, Equation of the circle is : [tex]x^{2} + 10x + y^{2} -4y -7 =0[/tex]
