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What is the equation of a circle when its diameter endpoints are at 2 -3 and 8 7?
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
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What is the equation of a circle when the endpoints of its diameter are at 10 -4 and 2 2 on the Cartesian plane?
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
If you Give a circle with a diameter of 4 what is the circumference?
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
What is the equation for the radius of a circle?
The radius of a circle = the diameter of the circle divided by 2
How do you find the area of a circle using its diameter?
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
How many radii of a circle will equal its circumference?
Well, the equation for finding the circumfrence of a circle is (diameter)(pi). That is diameter times pi. since the diameter of a circle is 2 radii, we can say that there is 2(pi) radii in a circle.
