Question Detail
Question
Find the equation of the normal to the circle x² + y² + 3x - 2y = 0 at the point (0,0).
Correct Answer
Option A is the correct answer.
Detailed Explanation
The center of the circle is (-3/2, 1). The slope of the radius from the center to (0,0) is (0 - 1)/(0 + 3/2) = -1/(3/2) = -2/3. The normal to the circle is along the radius, so its slope is -2/3. Equation through (0,0): y = (-2/3)x → 3x - 2y = 0.
Hint
The normal to a circle at a point lies along the radius from the center to that point.