Question Detail

MTH 101 MTH 101 Past Questions Objective Question
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Question

A circle has its center on the y-axis and passes through (-1,3) and (2,5). Find the equation.
Options
A x² + y² + 3x - 29 = 0
B 2x² + 2y² - 19y + 37 = 0
Correct Answer
C 3x² + 3y² - 3x + 2y + 12 = 0
D 2x² + 2y² - 4x + 27 = 0
Correct Answer

Option B is the correct answer.

Detailed Explanation

Center on y-axis means (0,k). Distance to (-1,3) and (2,5) are equal: (0+1)² + (k-3)² = (0-2)² + (k-5)² → 1 + (k² - 6k + 9) = 4 + (k² - 10k + 25) → k² - 6k + 10 = k² - 10k + 29 → -6k + 10 = -10k + 29 → 4k = 19 → k = 19/4 = 4.75. Center (0, 19/4). Radius² = 1 + (19/4 - 3)² = 1 + (19/4 - 12/4)² = 1 + (7/4)² = 1 + 49/16 = 65/16. Equation: (x-0)² + (y-19/4)² = 65/16 → multiply by 16: 16x² + 16(y² - (19/2)y + 361/16) = 65 → 16x² + 16y² - 152y + 361 = 65 → 16x² + 16y² - 152y + 296 = 0 → divide by 8: 2x² + 2y² - 19y + 37 = 0.

Hint

Set center as (0,k) and use equal distances.

Question Info

Course: MTH 101
Topic: MTH 101 Past Questions
Type: Objective
Difficulty: Not specified
Question 458 of 696
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