Discover new information and insights with the help of IDNLearn.com. Join our platform to receive prompt and accurate responses from experienced professionals in various fields.

Write the standard form of the equation of the circle with the given characteristics. Center: (3, 9); Solution point: (−2, 21)

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].