Circle $x^2 + y^2 + 16x + 12y + c = 0$ is touched by a straight line with slope $2$ and $y$-intercept $5$ units at a point $Q$. Then the coordinates of $Q$ are
Step-by-Step Solution
Key Concept: The tangent line at a point on a circle must satisfy both the point being on the circle and the tangency condition.
A line touches the given circle at point $(x_i, y_i)$ with equation $y_i = 2x_i + 5$. Substituting into the circle equation and using the condition $(y_i + 6) \times 2 = -1$ from the tangency constraint, we solve to get $x_i = -6$ and $y_i = -7$.
Correct Answer: 1