Multiple choice

For the line $3x+2y=12$ and the circle $x^2+y^2-4x-6y+3=0$, which of the following statements is true?

  1. Line is a tangent to the circle

  2. Line is a chord of the circle

  3. Line is a diameter of the circle

  4. None of these
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A Correct answer
AI explanation

Finding the center and radius of the circle from its equation gives the center at (2, 3) and a radius of 4. Using the perpendicular distance from a point to a line formula, the distance from the center (2, 3) to the line 3x + 2y - 12 = 0 calculates to 4, which equals the radius of the circle. Since the distance from the center to the line exactly equals the radius, the line is a tangent to the circle.

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