Question Detail

MTH 101 Analytical Geometry - The Circle Objective Question
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Question

What is the equation of a circle passing through the ends of a diameter with endpoints A(x₁, y₁) and B(x₂, y₂)?
Options
A (x - x₁)(x - x₂) - (y - y₁)(y - y₂) = 0
B (x - x₁)(x - x₂) + (y - y₁)(y - y₂) = 0
Correct Answer
C (x + x₁)(x + x₂) + (y + y₁)(y + y₂) = 0
D xx₁ + yy₁ = a²
Correct Answer

Option B is the correct answer.

Detailed Explanation

The equation of a circle through the ends of a diameter A(x₁,y₁) and B(x₂,y₂) is (x - x₁)(x - x₂) + (y - y₁)(y - y₂) = 0.

Hint

This equation is derived from the property that the angle in a semicircle is a right angle, leading to perpendicular slopes.

Question Info

Course: MTH 101
Topic: Analytical Geometry - The Circle
Type: Objective
Difficulty: Not specified
Question 310 of 696
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