GMAT® Practice : Coordinate Geometry

Concept: Equation of a circle

The question given below is a GMAT Math problem solving qusetion in Coordinate Geometry. The radius of the circle and the coordinates of the center of the circle are provided. The task is to find the equation of the circle.

Question: 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

Explanatory Answer

Video explanation will be added soon

Generalized form of equation of a circle

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

Choice E is the correct answer.

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