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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 (-4, 6.75)(4, 8)(4, 9.25)(4, 16), and its radius is 1.252.53.756.25 units. The equation of this circle in standard form is (x - 4)^2 + (y - 8)^2 = 2.5(x + 4)^2 + (y + 8)^2 = 2.5(x - 4)^2 + (y - 8)^2 = 6.25(x + 4)^2 + (y + 8)^2 = 6.25.

Respuesta :

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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