Answer:
[tex](x-2)^2+(y+5)^2=36[/tex]
Step-by-step explanation:
The standard form of a circle is given by the equation:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Where (h, k) is the center and r is the radius.
We know that the center is (2, -5). So, we can substitute 2 for h and -5 for k. This yields:
[tex](x-(2))^2+(y-(-5))^2=r^2[/tex]
Simplify:
[tex](x-2)^2+(y+5)^2=r^2[/tex]
Now, we need to determine r. We know that a point on the circle is (-4, -5). Thus, we can determine r by substituting -4 for x and -5 for y. This yields:
[tex](-4-2)^2+(-5+5)^2=r^2[/tex]
Evaluate:
[tex](-6)^2+(0)^2=r^2[/tex]
Evaluate:
[tex]36=r^2[/tex]
Hence, the radius squared is 36.
We do not actually need to solve for r, as we will square it anyways.
We will substitute 36 for r squared. Hence, our equation is:
[tex](x-2)^2+(y+5)^2=36[/tex]
The radius will thus be 6 units.
