Question

The diameter of Circle Q terminates on the circumference of the circle at (3,0) and (3,-7). Write the equation of the circle in standard form. Show all of your work for full credit.

Answer 1

Find the centre of the circle:

Centre of the circle is the midpoint of the diameter

Centre of the circle = ( (x1 + x2)/2 , (y1 + y2) /2 )

Centre of the circle = ( (3+3)/2 , (0-7)/2 )

Centre of the circle = ( 3 , -3.5 )

Find the length of the diameter:

Length = √[ (x1 - x2)² + (y1 - y2)² ]

Length = √[ (3 - 3)² + (0 + 7)² ]

Length = √7²

Length = 7

Find the radius:

Radius = Diameter ÷ 2

Radius = 7 ÷ 2

Radius = 3.5 units

Find the equation:

(x – h)² + (y – k)² = r²  where h and k is the centre of the circle

(x - 3)² + (y + 3.5)² = 3.5²

Answer:  (x - 3)² + (y + 3.5)² =  3.5²