Higher November 2017 Paper 3 Q19
19 Prove algebraically that the straight line with equation \(x - 2y = 10\) is a tangent to the circle with equation \(x^2 + y^2 = 20\) (5)
| Answer | Mark | Notes |
|---|---|---|
| Proof (supported) | M1 | starts process to find point of intersection by substituting, eg \((10 + 2y)^2 + y^2\ (= 20)\) |
| M1 | for expanding, eg \(4y^2 + 20y + 20y + 100\) (3 out of 4 terms correct) | |
| M1 | (dep M2) for 3-term quadratic equation ready for solving, eg \(5y^2 + 40y + 80 = 0\) | |
| M1 | (dep on previous M1) for method to solve an equation of the form \(ay^2 + by + c = 0\), eg by factorising or correct substitution into quadratic formula | |
| C1 | fully correct method leading to \(y = -4\) or \(x = 2\) or \((y + 4)^2 = 0\) or \((x - 2)^2 = 0\) and statement, eg only one point of intersection so the line is a tangent to the circle |