Answered

Discover the answers you need at Westonci.ca, a dynamic Q&A platform where knowledge is shared freely by a community of experts. Get quick and reliable solutions to your questions from a community of seasoned experts on our user-friendly platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

Select the correct answer from each drop-down menu.
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.

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

#SPJ1

We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.