The endpoints of a diameter of a circle are located at (5,9) and (11, 17). What is the equation of the circle?

loddsalgg6lu

loddsalgg6lu

Answered question

2023-03-22

The endpoints of a diameter of a circle are located at (5,9) and (11, 17). What is the equation of the circle?

Answer & Explanation

tambulloc5dn

tambulloc5dn

Beginner2023-03-23Added 8 answers

If a circle's diameter has endpoints at (5, 9) and (11, 17), the center is determined by the midpoint of line joining them i.e. ( 5 + 11 2 , 9 + 17 2 ) i.e. (8,13).
Radius is distance between (8,13) and (5,9)i.e. ( 8 - 5 ) 2 + ( 13 - 9 ) 2 = 9 + 16 = 25 = 5 .
Hence equation of circle is
( x - 8 ) 2 + ( y - 13 ) 2 = 25
x 2 - 16 x + 64 + y 2 - 26 y + 169 = 25
x 2 + y 2 - 16 x - 26 y + 208 = 0

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