Question Detail

MTH 101 Analytical Geometry - The Circle Objective Question
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Question

The ends of a diameter of a circle are (5,4) and (-3,6). What is the equation of the circle?
Options
A x² + y² - 2x - 10y + 9 = 0
Correct Answer
B x² + y² + 2x + 10y + 9 = 0
C x² + y² - 2x + 10y - 9 = 0
D x² + y² + 2x - 10y - 9 = 0
Correct Answer

Option A is the correct answer.

Detailed Explanation

Substituting (5,4) and (-3,6) into (x - x₁)(x - x₂) + (y - y₁)(y - y₂) = 0 gives (x-5)(x+3) + (y-4)(y-6) = 0. Expanding: x² -2x -15 + y² -10y +24 = 0, which simplifies to x² + y² - 2x - 10y + 9 = 0.

Hint

Use the formula (x - x₁)(x - x₂) + (y - y₁)(y - y₂) = 0 with the given points.

Question Info

Course: MTH 101
Topic: Analytical Geometry - The Circle
Type: Objective
Difficulty: Not specified
Question 311 of 696
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