Answer:
Standard Equation:
[tex](x+2)^{2}+(y+6)^{2}=100[/tex]
General Form:
[tex]x^{2}+4x+y^{2}+12y-60=0[/tex]
Step-by-step explanation:
The standard equation for a circle is [tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]
where,
x = x coordinate of circle point
h = x coordinate of center point
y = y coordinate of circle point
k = y coordinate of center point
r = radius of the circle
Whereas, the general form is [tex]x^{2} + y^{2} + Dx + Ey + F = 0[/tex] in which D, E, F are constants.
Since the diameter is given instead of a radius, divide the diameter by two.
Thus, r= 20/2 = 10.
So after substituting h=−2, k=−6, and r=10 into the formula above, we have the standard equation:
[tex](x-h)^{2}+(y-k)^{2}=r^{2}\\(x-(-2))^{2}+(y-(-6))^{2}=10^{2}\\(x+2)^{2}+(y+6)^{2}=100[/tex]
To find the general form, we will expand the standard form and bring all terms to the left side.
[tex](x+2)^{2}+(y+6)^{2}=100\\x^{2}+4x+4+y^{2}+12y+36-100=0\\x^{2}+y^{2}+4x+12y-60=0[/tex]
