The diameter of a circle has length 12. The center is at*(-5, 2). Give the equation
of the circle.

The equation of the circle with diameter of 12 and centre at (-5, 2) is;

x² + y² + 10x - 4y - 7 = 0

We are given;

Diameter of circle; d = 12

Thus; radius; r = d/2 = 12/2 = 6

Coordinates of center of circle = (-5, 2)

Formula for equation of a circle is given as;

(x - a)² + (y - b)² = r²

where (a, b) represents the coordinates of the center of the circle.

Thus;

(x - (-5))² + (y - 2)² = 6²

Expanding the bracket gives us;

x² + 10x + 25 + y² - 4y + 4 = 36

x² + y² + 10x - 4y + 29 = 36

x² + y² + 10x - 4y + 29 - 36 = 0

x² + y² + 10x - 4y - 7 = 0

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Equation of the circle is :

Step-by-step explanation:

Let us consider the image attached in the answer area.

The center O has the co-ordinates i.e. (-5,2) and the diameter given is 12 units.

We know that radius is half of diameter.

The equation for circle given the center and radius, can be represented as:

Where (a,b) is the co-ordinate of center and r is the radius.

Let us consider the following formula:

Hence, Equation of the circle is :

sss (side, side, side)

sas (side, angle, side)

asa (angle, side, angle)

aas (angle, angle, side)

hl (hypotenuse, leg)

your answer would be 12