Question

The endpoints of the longest chord on a circle are (4, 5.5) and (4, 10.5).the center of the circle is at the point , and its radius is units. the equation of this circle in standard form is .

Answer 1

The midpoint of the points ( 4, 5.5 ) and ( 4, 10.5 ) is the center of the circle:
C =
`((4+4)/(2), (5.5+10.5)/(2))`
C = ( 4, 8 ), h=4, k=8
r =
`\sqrt{(4-4)^(2) +(8-5.5)^(2) } = \sqrt{0+2.5^(2) }`
r = 2.5
The equation of the circle in standard form:
( x - h )² + ( y - k )² = r²
( x - 4 )² + ( y - 8 ) = 6.25