## Exam-Style Question on Parametric Equations## A mathematics exam-style question with a worked solution that can be revealed gradually |

Question id: 626. This question is similar to one that appeared on an A-Level paper in 2017. The use of a calculator is allowed.

The curve C has parametric equations

\(x=2t+3, \quad y=7-2t^2\)

(a) Find the cartesian equation for C in its simplest form.

(b) Find \( \dfrac{dy}{dx} \)

The point \(P\) lies on C where \(t = 3\)

(c) Find the equation of the tangent to C at the point \(P\). Give your answer in the form \(y = ax + b\), where \(a\) and \(b\) are integers to be determined.

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