Question

The equation of a circle is given below.

\left(x-\dfrac23 \right)^{2}+y^{2} = 36(x−
3
2
​
)
2
+y
2
=36left parenthesis, x, minus, start fraction, 2, divided by, 3, end fraction, right parenthesis, squared, plus, y, squared, equals, 36
What is its center?
((left parenthesis
,,comma
))right parenthesis
What is its radius?
If necessary, round your answer to two decimal places.
units

Answer 1

Center = 2/3,0 R=6

Explanation:

Answer 2

The center of the circle is (2/3, 0) and radius is ±6units

Explanation:

Given the equation of a circle given as shown;

(x-2/3)²+y² = 36

To get the radius and centre of the circle, we will compare the equation with the general equation of a circle given as;

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

Comparing with the given equation,

we will see that;

a = 2/3, b = 0 and r² = 36

If r² = 36

r = ±√36

r = ±6

This shows that the center of the circle (a, b) = (2/3, 0) and radius is ±6