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Sagot :
The correct options regarding the circle with endpoints of the longest chord at (4, 5.5) and (4, 10.5) are:
- The center is (4,8).
- The radius is of 2.5 units.
- [tex](x - 4)^2 + (y - 8)^2 = 6.25[/tex]
What is the equation of a circle?
The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
The center is the midpoint of the chords, hence:
- [tex]x_0 = \frac{4 + 4}{2} = 4[/tex].
- [tex]y_0 = \frac{5.5 + 10.5}{2} = 8[/tex].
The radius is half the distance between the chords, hence:
[tex]r = 0.5\sqrt{(4-4)^2 + (10.5 - 5.5)^2} = 0.5 = 2.5[/tex].
Hence the equation is:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
[tex](x - 4)^2 + (y - 8)^2 = 2.5^2[/tex]
[tex](x - 4)^2 + (y - 8)^2 = 6.25[/tex]
More can be learned about the equation of a circle at https://brainly.com/question/24307696
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