Question

Write the equation of the circle graphed below

Answer 1

Answer:

$(x-1)^2+(y+1)^2=0.25$

Step-by-step explanation:

From the given graph it is clear that the center of the circle is (1,-1) and the circle passing through the point (0.5,-1).

So, radius of the circle is  

$r=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$r=\sqrt{(0.5-1)^2+(-1-(-1))^2}$

$r=\sqrt{(-0.5)^2}$

$r=\sqrt{(0.5)^2}$

$r=0.5$

The radius of the circle is 0.5 units.

The standard form of a circle is  

$(x-h)^2+(y-k)^2=r^2$

where, (h,k) is center and r is radius.

The center of given circle is (1,-1) and radius is 0.5. So, the equation of circle is

$(x-(1))^2+(y-(-1))^2=(0.5)^2$

$(x-1)^2+(y+1)^2=0.25$

Therefore, the required equation is $(x-1)^2+(y+1)^2=0.25$.