Question Detail
Question
Find the equation of the normal to the circle x² + y² + 3x - 2y = 0 at the point (3,2).
Correct Answer
Option B is the correct answer.
Detailed Explanation
First verify that (3,2) is on the circle: 9+4+9-4=18 ≠ 0, so (3,2) is not on the circle. There might be an error. If we proceed, the circle can be written as (x+3/2)² + (y-1)² = 13/4. Center = (-3/2, 1). The slope from center to point is (2-1)/(3+3/2) = 1/(4.5) = 2/9. Normal slope = -9/2. Equation through (3,2): y-2 = (-9/2)(x-3) → 2y-4 = -9x+27 → 9x+2y-31=0. None match exactly. Option B: 9x-2y+12=0 has slope 9/2, not -9/2.
Hint
The normal line passes through the point and is perpendicular to the radius.