Question Detail
Question
Find the equation of the tangent to the circle x² + y² + 4x - 2y - 15 = 0 at (2,3).
Correct Answer
Option A is the correct answer.
Detailed Explanation
First verify that (2,3) lies on the circle: 4+9+8-6-15=0, yes. For circle x²+y²+2gx+2fy+c=0, equation of tangent at (x1,y1) is xx1+yy1+g(x+x1)+f(y+y1)+c=0. Here 2g=4→g=2, 2f=-2→f=-1, c=-15. Tangent: 2x + 3y + 2(x+2) -1(y+3) -15 = 0 → 2x+3y+2x+4 -y-3 -15 = 0 → 4x+2y -14 = 0 → divide by 2: 2x + y -7 = 0 → 2x+y=7.
Hint
Use the tangent formula for circles.