Higher November 2020 Paper 4 Q18
18 Here is a sketch of the circle \(x^2 + y^2 = 45\).
(a) Show that the tangent to this circle at the point (−3, 6) has a gradient of \(\frac{1}{2}\). [2]
(b) Find the equation of the tangent at the point (−3, 6). [2]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(\frac{6}{-3}\) or −2 and | 1 | accept any correct method | Only award full marks if no wrong working |
| \(\frac{-1}{\textit{their}\ -2}\) [\(= \frac{1}{2}\)] oe | 1 | condone \(\frac{-6}{3}\) for first mark | |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(y = \frac{1}{2}x + 7\frac{1}{2}\) oe | 2 | B1 for \(y = \frac{1}{2}x + c\) or \(y = mx + 7\frac{1}{2}\) or the equation of any line which goes through (−3, 6) | where \(m \ne 0\) |