Get the answers you need at Westonci.ca, where our expert community is always ready to help with accurate information. Discover comprehensive answers to your questions from knowledgeable professionals on our user-friendly platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.
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
Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.
