Higher June 2017 Paper 1 Q27
27 \(P\,(-1, 4)\) is a point on a circle, centre \(O\)
Not drawn accurately
Work out the equation of the tangent to the circle at P.
Give your answer in the form \(\quad y = mx + c\) [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(\dfrac{4 - 0}{-1 - 0}\) or \(-4\) | M1 | oe |
| \(-1 \div\) their \(-4\) or \(\dfrac{1}{4}\) | M1 | oe their \(-4\) must be their gradient of OP |
| \(y - 4 = \) their \(\dfrac{1}{4}(x - -1)\) or \(4 = \) their \(\dfrac{1}{4}(-1) + c\) | M1dep | oe dep on second M1 oe \(c = 4.25\) |
| \(y = \dfrac{1}{4}x + \dfrac{17}{4}\) or \(y = 0.25x + 4.25\) | A1 | oe eg \(\;y = 0.25x + 4\dfrac{1}{4}\) Accept \(\;y = \dfrac{x + 17}{4}\) |
Additional guidance
| An answer of \(4y = x + 17\), with or without the correct answer seen | M1M1M1A0 |
| For A1, allow a mixture of fractions, decimals and mixed numbers | |
| \(y - y_1 = m(x - x_1)\) stated, followed by \(\;y - 4 = \dfrac{1}{4}(x - -1)\) oe | M1M1M1 |