Higher June 2017 Paper 2 Q23
23 L is the circle with equation \(x^2 + y^2 = 4\)
\(P\left(\dfrac{3}{2}, \dfrac{\sqrt{7}}{2}\right)\) is a point on L.
Find an equation of the tangent to L at the point \(P\). (3)
| Answer | Mark | Notes |
|---|---|---|
| \(y = \dfrac{-3}{\sqrt{7}}x + \dfrac{8}{\sqrt{7}}\) | M1 | for method to find gradient of \(OP\), eg \(\dfrac{\sqrt{7}}{2} \div \dfrac{3}{2}\ \left(= \dfrac{\sqrt{7}}{3} \text{ or } 0.88\ldots\right)\) oe |
| M1 | (dep) for method to find gradient of tangent, \(m\), eg. \(\dfrac{\frac{\sqrt{7}}{2}}{\frac{3}{2}} \times m = -1\ \left(m = \dfrac{-3}{\sqrt{7}} \text{ or } -1.13\ldots\right)\) | |
| A1 | for \(y - \dfrac{\sqrt{7}}{2} = \dfrac{-3}{\sqrt{7}}\left(x - \dfrac{3}{2}\right)\) or \(y = \dfrac{-3\sqrt{7}}{7}x + \dfrac{8\sqrt{7}}{7}\) oe or \(y - 1.32\ldots = -1.13\ldots(x - 1.5)\) |