Question Detail
Question
What is the equation of the tangent line to the curve \( x^2 + y^2 = 169 \) at the point \( (5, -12) \)?
Correct Answer
Option A is the correct answer.
Detailed Explanation
Using implicit differentiation: ( 2x + 2y \frac{dy}{dx} = 0 \implies \frac{dy}{dx} = -\frac{x}{y} ). At ( (5, -12) ), slope ( m = -\frac{5}{-12} = \frac{5}{12} ). Line: ( y - (-12) = \frac{5}{12}(x - 5) \implies 12y + 144 = 5x - 25 \implies 5x - 12y = 169 ).
Hint
Use implicit differentiation to find the slope of the curve at the given point.