Higher November 2022 Paper 2 Q24
24 A circle has equation \(x^2 + y^2 = 12.25\)
The point \(P\) lies on the circle.
The coordinates of \(P\) are \((2.1, 2.8)\)
The line L is the tangent to the circle at point \(P\).
Find an equation of L.
Give your answer in the form \(ax + by = c\), where \(a\), \(b\) and \(c\) are integers. (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| \(6x + 8y = 35\) | M1 | for a process to find the gradient of the radius, eg \(\dfrac{2.8 - 0}{2.1 - 0}\ \left(= \dfrac{4}{3}\right)\) |
| M1 | for process to find the gradient of the tangent, eg uses \(\dfrac{-1}{\text{``}m\text{''}}\) | |
| M1 | for substitution of \((2.1, 2.8)\) into \(y = \text{``}{-}\dfrac{3}{4}\text{''}x + c\) or into \((y - y_1) = \text{``}{-}\dfrac{3}{4}\text{''}(x - x_1)\) | |
| A1 | oe as long as in the form \(ax + by = c\), where \(a\), \(b\) and \(c\) are integers |