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A. Rhoda's circular garden in San Nicolas is enclosed in a 6 m by 6 m square lot. If this will be illustrated on the Cartesian plane, the garden is located on the first quadrant. If the circular garden is tangential to the axes of the plane, find the equation of the circular garden.​

PASEND ANSWER ASAPA Rhodas Circular Garden In San Nicolas Is Enclosed In A 6 M By 6 M Square Lot If This Will Be Illustrated On The Cartesian Plane The Garden I class=

Sagot :

The diameter of the circular garden is equal to the side length of the

square lot.

Response:

  • The equation of the circular garden is; (x - 3)² + (y - 3)² = 3²

Method used to derive the equation of the circle

The given parameters are;

The size of the square lot enclosing the garden = 6 m by 6 m

Location of the garden = The first quadrant

The garden is tangential to the axes of the plane, therefore, the tangents are the axes of the plane.

Required:

To find the equation of the circular garden.

Solution:

The diameter of a circle inscribed in a square is equal to the side length of the square, therefore;

Diameter of the circular garden = 6 meters

[tex]Radius = \mathbf{ \dfrac{Diameter}{2}}[/tex]

[tex]Radius \ of \ the \ circular \ garden = \dfrac{6 \, m}{2} = 3 \, m[/tex]

Therefore, the center of the circle is a radii length from each axis, which gives;

The center of the circle = (3, 3)

The general equation of a circle is presented as follows;

(x - h)² + (y - k)² = r²

Where:

(h, k) = The coordinates of the center of the circle = (3, 3)

The equation of the circle is therefore;

  • [tex]\underline{(x - 3)^2 + (y - 3)^2 = 3^2}[/tex]

Learn more about the properties of a circle here:

https://brainly.com/question/6320762

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