Higher November 2019 Paper 1 Q21
21. In this question, all lengths are in centimetres.
A circle has equation \(x^2 + y^2 = 49\).
Points A, B and C all lie on this circle.
Their co-ordinates are A \((a, 0)\), B \((b, 0)\) and C \((0, c)\), where \(a \lt 0\), \(b \gt 0\) and \(c \gt 0\).
(a) Find the length of the line AB. [2]
(b) The tangent to the circle at A and the tangent to the circle at C meet at the point T.
Find the coordinates of T. [2]
Find the coordinates of T. [2]
| Scheme | Marks | Comments |
|---|---|---|
| 14 | B2 | B1 for \(2 \times \sqrt{49}\) or for radius = 7 si |
| Scheme | Marks | Comments |
|---|---|---|
| \((-7, 7)\) | B2 | FT ‘their derived radius’ from part (a) B1 for T \(\left(-\sqrt{49}, \sqrt{49}\right)\) or equations of tangents stated as \(x = -7\) and \(y = 7\) or clear sketch with correct intersecting tangents marked and axes appropriately numbered. NB Sketch may be in answer space for part (a). |
| (4) |