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radius = ½ diameter

= ½ Distance between endpoints

= ½√((difference in x)² + (difference in y)²)

= ½√((8 - 2)² + (7 - -3)²)

= ½√(6² + 10²)

= ½√136

Centre of circle = midpoint of diameter

= (mean average of x, mean average of y)

= ((2 + 8)/2, (-3 + 7)/2)

= (5, 2)

Circle with centre (Xc, Yc) and radius r has equation:

(x - Xc)² + (y - Yc)² = r²

Which for circle with centre (5, 2) and radius ½√136 gives:

(x - 5)² + (y - 2)² = (½√136)² = ¼ × 136 = 34

→ (x - 5)² + (y - 2)² = 34

This can be expanded and rearranged to get:

x² -10x + 25 + y² - 4y + 4 - 34 = 0

→ x² - 10x + y² - 4y - 5 = 0

Q: What is the equation of a circle when its diameter endpoints are at 2 -3 and 8 7?

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Endpoints: (10, -4) and (2, 2) Midpoint: (6, -1) which is the centre of the circle Distance from (6, -1) to (10, -4) or (2, 2): 5 which is the radius of the circle Therefore equation of the circle: (x-6)^2 + (y+1)^2 = 25

the equation for the circumference of a circle is 2*radius*pi, or since the radius is half of the diameter 2*radius=diameter, we can simplify the equation to the circumference of a circle=diameter*pi

The radius of a circle = the diameter of the circle divided by 2

The area of a circle is pi(radius)2 Radius is half the diameter. Simply divide the diameter in half and enter it into the equation 3.14(diameter/2)2

It works out as the square root of 5 or about 2.236 to three decimal places

Related questions

Yes, it have.

Endpoints: (10, -4) and (2, 2) Midpoint: (6, -1) which is the centre of the circle Distance from (6, -1) to (10, -4) or (2, 2): 5 which is the radius of the circle Therefore equation of the circle: (x-6)^2 + (y+1)^2 = 25

Diameter endpoints: (2, 7) and (-6, -1) Centre of circle will be the midpoint which is: (-2, 3)

The equation works out as: (x-1)2+(y+0.5)2 = 18.25 Equation of a circle: (x-a)2+(y-b)2 = radius2 whereas a and b are the coordinates of the circle's centre

Endpoints: (2, 2) and (10, -4) Midpoint: (6, -1) which is the centre of the circle Distance from (6, -1) to (2, 2) or (10, -4) = 5 which is the radius of the circle Therefore equation of the circle: (x-6)^2 + (y+1)^2 = 25

dinosaurs

The equation works out as: (x-1)2+(y-4)2 = 25 whereas (1, 4) is the circle's centre and 25 is the radius2

Endpoints: (2, -3) and (8, 7)Centre of circle: (5, 2)Radius of circle is the square root of 34Equation of the circle: (x-5)^2 +(y-2)^2 = 34Slope of radius: 5/3Slope of tangents: -3/51st tangent equation: y--3 = -3/5(-2) => 5y = -3x-92nd tangent equation: y-7 = -3/5(x-8) => 5y = -3x+59

the equation for the circumference of a circle is 2*radius*pi, or since the radius is half of the diameter 2*radius=diameter, we can simplify the equation to the circumference of a circle=diameter*pi

The radius of a circle = the diameter of the circle divided by 2

Diameter = 1/2 of the circle's radius. Diameter = 2 times the square root of (the circle's area/pi) Diameter = the circle's circumference/pi

Endpoints of diameter: (-10, -2) and (4, 6)Midpoint which is the center of the circle: (-3, 2)Radius of the circle: square root of 65Equation of the circle: (x+3)^2 +(y-2)^2 = 65