standard form of circle is (x−h)^2+(y−k)^2=r^2 here (h,k) is the centre and r is the radius

the centre of the circle is the midpoint of diameter...

since the diameter points are given Apply the Midpoint Formula,to find the centre

centre of circle= centre of the two points (9,2) and (-1,4)

centre of circle= ((9+ -1)/2, (2+ 4)/2)

= (4, 3).........

radius = distance between centre and one of the cordinates through which circle passes

= distance between (4, 3) and (9,2)

= √ (9-4)^2+ (3-2)^2

= √26......................

now standard form of circle is (x−h)^2+(y−k)^2=r^2

(x- 4)^2 + ( y- 3 )^2 = (√26)^2

(x- 4)^2 + ( y- 3 )^2 = √26............................................................ANSWER

hope you understand..please message if you have any doubts..thank you

(x- 4)^2 + ( y- 3 )^2 = 26....................................answer (square root not there..i typed wrongly in previous submit)

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