Question Detail

MTH 101 Analytical Geometry - The Circle Objective Question
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Question

Find the centre and radius of the circle with equation x² + y² + 3x - 2y + 2 = 0 using the perfect square method.
Options
A Centre (-3/2, 1), Radius = √5/2
Correct Answer
B Centre (3/2, -1), Radius = √5/2
C Centre (-3/2, -1), Radius = 5/2
D Centre (3/2, 1), Radius = 5/2
Correct Answer

Option A is the correct answer.

Detailed Explanation

Completing the square: (x² + 3x) + (y² - 2y) = -2. This becomes (x + 3/2)² + (y - 1)² = -2 + 9/4 + 1 = 5/4. Thus, centre is (-3/2, 1) and radius is √(5/4) = √5/2.

Hint

Complete the square for the x terms and y terms to rewrite the equation in the form (x - a)² + (y - b)² = r².

Question Info

Course: MTH 101
Topic: Analytical Geometry - The Circle
Type: Objective
Difficulty: Not specified
Question 303 of 696
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