Question Detail

MTH 101 MTH 101 Past Questions Objective Question
Take CBT

Question

Find the equation of a circle whose diameter has the ends (-5, 1) and (3, -7).
Options
A x² + y² - 5x - 4y - 15 = 0
B x² + y² - 2x - 10y + 9 = 0
C x² + y² + 2x + 6y - 22 = 0
Correct Answer
D x² + y² - 2x - 6y + 22 = 0
Correct Answer

Option C is the correct answer.

Detailed Explanation

Center is midpoint: ((-5+3)/2, (1+(-7))/2) = (-2/2, -6/2) = (-1, -3). Radius = half the distance between endpoints: distance = √[(3-(-5))² + (-7-1)²] = √[8² + (-8)²] = √(64+64) = √128 = 8√2. Radius = 4√2. Equation: (x+1)² + (y+3)² = 32 → x² + 2x + 1 + y² + 6y + 9 = 32 → x² + y² + 2x + 6y + 10 - 32 = 0 → x² + y² + 2x + 6y - 22 = 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 496 of 696
Previous Course Details Next