Equation of a Circle
Given a circle with its center at (h,k) and a radius r, the equation of the circle is given as:
[tex](x-h)^2+(y-k)^2=r^2[/tex]We are given a circle and two points on its circumference. We'll assume they define two radii that are perpendicular to each other.
The difference between the x-coordinates of the points is 7-4=3
The difference between the y-coordinates of the points is 7-4=3
This gives us the coordinates of the center as (4,4) and the radius r=3
Substituting in the equation above:
[tex](x-4)^2+(y-4)^2=3^2=9[/tex]Expanding the squares:
[tex]x^2-8x+16+y^2-8y+16=9[/tex]Simplifying:
[tex]x^2-8x+y^2-8y+32=9[/tex]Rearranging:
[tex]x^2+y^2-8x-8y+32=9[/tex]Choice B
