Standard +0.8 This question requires completing the square to find the circle's center and radius, recognizing the geometric configuration of tangents from an external point, then applying trigonometry (likely using right triangles formed by the center, point of tangency, and external point) to find the angle between tangents. It combines multiple techniques across coordinate geometry and trigonometry with some problem-solving insight needed for the geometric setup, making it moderately challenging but still within standard A-level scope.
In this question you must show detailed reasoning.
A circle has equation \(x^2 + y^2 - 6x - 4y + 12 = 0\). Two tangents to this circle pass through the point \((0, 1)\).
You are given that the scales on the \(x\)-axis and the \(y\)-axis are the same.
Find the angle between these two tangents. [7]
In this question you must show detailed reasoning.
A circle has equation $x^2 + y^2 - 6x - 4y + 12 = 0$. Two tangents to this circle pass through the point $(0, 1)$.
You are given that the scales on the $x$-axis and the $y$-axis are the same.
Find the angle between these two tangents. [7]
\hfill \mbox{\textit{SPS SPS SM 2023 Q10 [7]}}