Question

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

Answer 1

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).

$r=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$r=\sqrt{(-2-3)^2+(21-9)^2}$

$r=\sqrt{(-5)^2+(12)^2}$

$r=\sqrt{25+144}$

On further simplification, we get

$r=\sqrt{169}$

$r=13$

The radius of the circle is 13 units.

The standard form of a circle is

$(x-h)^2+(y-k)^2=r^2$

Where, (h,k) is the center and r is the radius.

Putting h=3, k=9 and r=13, we get

$(x-3)^2+(y-9)^2=(13)^2$

$(x-3)^2+(y-9)^2=169$

Therefore, the standard form of the circle is $(x-3)^2+(y-9)^2=169$.