Question

Determine the equation of the circle graphed below.

Answer 1

Answer:

Equation = (x - 6 )² + ( y + 3 )² = 9

Step-by-step explanation:

The circle passes through ( 6, 0) and  ( 6 , -6)

They are the coordinates of the diameter.

Using this we can find the centre of the circle.

Find the centre of the circle.

Centre of the circle is the mid- point of (6, 0) and ( 6, -6)

      $Centre = (\frac{x_1+x_2}{2} , \frac{y_1 + y_2}{2})$

                 $=(\frac{6 + 6}{2}, \frac{0 + (-6)}{2})\\\\=(6, -3)$

Find the radius of the circle.

$Radius = \frac{Diameter }{2}$

Diameter is the distance between the points (6 , 0) and ( 6, - 6)

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

               $=\sqrt{(6-6)^2 + (-6 -0)^2}\\\\=\sqrt{0 + 36} \\\\= 6$

Therefore,

    $Radius ,r = \frac{6}{2} = 3$

Standard equation of a circle:

$(x - a)^2 + (y - b)^2 = r^2 \ where \ (a , b) \ is \ the\ centre \ coordinates.$

Therefore , equation of the circle ;

                    $(x - 6)^2 + (y + 3)^2 = 3^2\\\\(x -6)^2 + (y + 3)^2 = 9$