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You are here: Home » GMAT Test Prep Questions » Coordinate Geometry » Question 1

The question given below is a Math problem in Coordinate Geometry and requires using the distance formula to determine the locus of a point.

Question 1

What is the equation of a circle of radius 6 units centered at (3, 2)?

1. x² + y² + 6x - 4y = 23
2. x² + y² - 6x + 4y = 23
3. x² + y² + 6x + 4y = 23
4. x² + y² - 6x - 4y = -23
5. x² + y² - 6x - 4y = 23

The correct choice is (E) and the correct answer is x² + y² - 6x - 4y = 23.

Explanatory Answer

Equation of a circle with center (a, b) and radius 'r' units is (x - a)² + (y - b)² = r²

Therefore, the equation of this circle = (x - 3)² + (y - 2)² = 6²

i.e., x² - 6x + 9 + y² - 4y + 4 = 36

or x² + y² - 6x - 4y = 23