IDNLearn.com: Your one-stop platform for getting reliable answers to any question. Get prompt and accurate answers to your questions from our community of experts who are always ready to help.
Sagot :
Given:
Center of a circle is (3,9).
Solution point is (-2,21).
To find:
The standard form of the circle.
Solution:
Radius is the distance between center (3,9) and the solution point (-2,21).
[tex]r=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]r=\sqrt{(-2-3)^2+(21-9)^2}[/tex]
[tex]r=\sqrt{(-5)^2+(12)^2}[/tex]
[tex]r=\sqrt{25+144}[/tex]
On further simplification, we get
[tex]r=\sqrt{169}[/tex]
[tex]r=13[/tex]
The radius of the circle is 13 units.
The standard form of a circle is
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Where, (h,k) is the center and r is the radius.
Putting h=3, k=9 and r=13, we get
[tex](x-3)^2+(y-9)^2=(13)^2[/tex]
[tex](x-3)^2+(y-9)^2=169[/tex]
Therefore, the standard form of the circle is [tex](x-3)^2+(y-9)^2=169[/tex].
We appreciate your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. IDNLearn.com is committed to providing the best answers. Thank you for visiting, and see you next time for more solutions.