Question

Write an equation of the circle given its center and radius

Answer 1

(x-2)²+(y-3)² = 0.25

Explanation:

We have given that

Center = (2,3) ; Diameter = 1

We have to find the equation of circle.

The standard equation of circle is:

(x-a)²+(y-b)² = r² where (a,b) is the center of circle and r is the radius.

Radius is half of the diameter of circle.

r = d/2

r = 1/2

(a,b) = (2,3)

Putting values in above formula, we have

(x-2)²+(y-3)² = (1/2)²

(x-2)²+(y-3)² = 1/4

(x-2)²+(y-3)² = 0.25 which is the equation of circle.

Answer 2

Answer:

x²+y²-4x-6y+12.75=0

Explanation:

The equation is given by (x-h)²+(y-k)²=r²

center is (2,3), so h=2, k=3,r=0.5

equation is given by;

(x-2)²+(y-3)²=0.5²

Expand

x(x-2)-2(x-2)+y(y-3)-3(y-3)=0.5²

4-2x-2x+x²+9-3y-3y+y²=0.25

4-4x+x²+9-6y+y²=0.25

x²-4x+13+y²-6y=0.25

x²-4x+y²-6y+13=0.25

x²-4x+y²-6y+12.75=0

x²+y²-4x-6y+12.75=0