plz answer these questions 15 18 22 19
Answers
Answer:
( x - 3 )² + ( y - 5 )² = 25
Hello. Hope this helps!
Step-by-step explanation:
The equation of a circle can be written in the form
( x - a )² + ( y - b )² = c²
where the centre is at ( a , b ) and the radius is c.
From here, the centres of the given circles are at ( 2, 4 ) and at ( 4, 6 ).
The midpoint of this segment is obtained by taking the average of the x-coordinates, and the average of the y-coordinates. So it is
( ( 2 + 4 ) / 2, ( 4 + 6 ) / 2 ) = ( 3, 5 )
We are told that this is the centre of our circle, so our circle has equation
( x - 3 )² + ( y - 5 )² = c²
for some c.
We're not told the radius directly, but we do have a point on the circle, which means that this point satisfies the equation. So we substitute ( x, y ) = ( 6, 1 ) into our equation to determine c².
c² = ( 6 - 3 )² + ( 1 - 5 )² = 9 + 16 = 25
Finally, the equation of our circle is
( x - 3 )² + ( y - 5 )² = 25
[ Incidentally, the radius of our circle is √25 = 5. ]