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Circle on diameter ends (x₁, y₁), (x₂, y₂) has which equation?
A(x+x₁)(x+x₂)+(y+y₁)(y+y₂)=0
B(x−x₁)(x−x₂)+(y−y₁)(y−y₂)=0
C(x−x₁)(y−y₁)+(x−x₂)(y−y₂)=0
D(x−x₁)²+(y−y₂)²+(x−x₂)²=0
Answer & Solution
Correct answer: B. (x−x₁)(x−x₂)+(y−y₁)(y−y₂)=0
Since the angle in a semicircle is a right angle, a point P on the circle gives perpendicular slopes PA and PB, which leads to the diameter form.
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