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What is the equation of a circle when its diameter endpoints are at 2 -3 and 8 7?
Wiki User
∙ 6y ago
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
Wiki User
∙ 6y ago
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Two of the endpoints of the diameter of a circle are at A -6 and 8 and B 6 and -8 1. determine the radius of the circle 2. state an equation of the circle I appreciate the help.?
dinosaurs
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