Question

Write the equation of the circle graphed below

Answer 1

Given:

Given that the circle is graphed with center (-1,1)

We need to determine the equation of the circle.

Radius:

To determine the radius of the circle, let us simply count the number of units between the center point to any point on the circle.

Hence, from the figure, it is obvious that there are 5 units between the center and any point on the circle.

Thus, radius of the circle is 5 units.

Equation of the circle:

The standard form for the equation of the circle is given by

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

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

Substituting the center (-1,1) and r = 5 in the above formula, we get;

$(x+1)^{2}+(y-1)^{2}=5^{2}$

$(x+1)^{2}+(y-1)^{2}=25$

Thus, the equation of the circle is $(x+1)^{2}+(y-1)^{2}=25$