Higher November 2023 Paper 4 Q20
20 The diagram shows a circle, centre the origin, with the tangent to the circle at the point (4, 2).
(a) Write down the equation of the circle. [2]
(b)
(i) Show that the tangent to the circle at the point (4, 2) has gradient −2. [2]
(ii) Find the equation of the tangent to the circle at the point (4, 2). [2]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(x^2 + y^2 = 20\) | 2 | B1 for \(x^2 + y^2 = k\) | \(k\) could be \(r^2\) or \(\sqrt{20}^{\,2}\) but not 20 |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| (i) [gradient =] \(\frac{2}{4}\) or \(\frac{1}{2}\) | M1 | ||
| \(m \times \textit{their}\ \frac{2}{4} = -1\) used or implied | M1 | If 0 scored SC1 for \(-\frac{4}{2}\) or \(-\frac{2}{1}\) without seeing \(\frac{2}{4}\) or \(\frac{1}{2}\) | for M1 allow \(-2 \times \frac{2}{4} = -1\) or e.g. \(-\frac{4}{2}\) after \(\frac{2}{4}\) seen or \(-\frac{2}{1}\) after \(\frac{1}{2}\) seen |
| (ii) \(y = -2x + 10\) oe | 2 | B1 for \(y = -2x + c\) seen oe or \(-2x + 10\) or \(c = 10\) | ‘c’ can be 0 but not 10 |