Standard +0.8 This question requires understanding that tangents are perpendicular to radii, finding the center by solving simultaneous equations of perpendicular lines through given points, then forming the circle equation. It involves multiple geometric concepts and algebraic steps beyond routine circle problems, but uses standard A-level techniques throughout.
In this question you must show detailed reasoning.
The lines \(y = \frac{1}{2}x\) and \(y = -\frac{1}{2}x\) are tangents to a circle at \((2, 1)\) and \((-2, 1)\) respectively. Find the equation of the circle in the form \(x^2 + y^2 + ax + by + c = 0\), where \(a\), \(b\) and \(c\) are constants. [6]
In this question you must show detailed reasoning.
The lines $y = \frac{1}{2}x$ and $y = -\frac{1}{2}x$ are tangents to a circle at $(2, 1)$ and $(-2, 1)$ respectively. Find the equation of the circle in the form $x^2 + y^2 + ax + by + c = 0$, where $a$, $b$ and $c$ are constants. [6]
\hfill \mbox{\textit{OCR PURE Q8 [6]}}