Challenging +1.2 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 using right-angled triangle trigonometry to find the angle. While it involves multiple steps and coordinate geometry combined with trigonometry, the techniques are all standard A-level methods with no novel insight required. The 7-mark allocation reflects moderate complexity, placing it above average difficulty.
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{OCR PURE Q8 [7]}}