Question Detail

MTH 101 MTH 101 Past Questions Objective Question
Take CBT

Question

The ends of a diameter have coordinates (5, 4) and (-3, 6). Find the equation of the circle.
Options
A x² + y² - 5x - 4y - 15 = 0
B x² + y² - 2x - 10y + 9 = 0
Correct Answer
C x² + y² - 3x - 6y - 2 = 0
D x² + y² - 6x - 8y + 15 = 0
Correct Answer

Option B is the correct answer.

Detailed Explanation

Center is midpoint of diameter: ((5+(-3))/2, (4+6)/2) = (2/2, 10/2) = (1, 5). Radius = half the distance between endpoints: distance = √[(5-(-3))² + (4-6)²] = √[8² + (-2)²] = √(64+4) = √68 = 2√17. Radius = √17. Equation: (x-1)² + (y-5)² = 17 → x² - 2x + 1 + y² - 10y + 25 = 17 → x² + y² - 2x - 10y + 26 - 17 = 0 → x² + y² - 2x - 10y + 9 = 0.

Hint

The center is the midpoint of the diameter endpoints.

Question Info

Course: MTH 101
Topic: MTH 101 Past Questions
Type: Objective
Difficulty: Not specified
Question 487 of 696
Previous Course Details Next