Answer:
[tex](x+1)^2 + (y+2)^2 = 85[/tex]
and B
Step-by-step explanation:
To write the equation of a circle, use the formula [tex](x-h)^2+(y-k)^2 = r^2[/tex] where the center of the circle is (h, k).
This means the equation is [tex](x--1)^2 + (y--2)^2 = r^2 \\\\ (x+1)^2 + (y+2)^2 = r^2[/tex].
Find the radius r by finding the distance between (-1,-2) and (6,4) using the distance formula.
[tex]d = \sqrt{(6--1)^2 + (4--2)^2} =\sqrt{(7)^2 + (6)^2} =\sqrt{49+36} =\sqrt{85}[/tex]
Since the radius is √85 and therefore [tex]r^2 = 85[/tex].
The equation is [tex](x+1)^2 + (y+2)^2 = 85[/tex].
To see what other point is on the circle, substitute the (x,y) in the equation.
(-10+1)^2 + (0+2)^2 = 85
81 + 4 = 85
85 = 85
The point (-10,0) is on the circle.
