A curve C1 C_1\,C1 with parametric equations
x=7cost,y=26sint0≤t<2π x = 7 \cos t, \quad y = 2\sqrt{6} \sin t \quad 0 \leq t < 2\pi x=7cost,y=26sint0≤t<2πmeets the circle C2 C_2\,C2 at four distinct points with Cartesian coordinates
(1435,2785),(1435,−2785),(−1435,2785),(−1435,−2785) \left(\frac{14\sqrt{3}}{5}, \frac{2\sqrt{78}}{5}\right),\quad \left(\frac{14\sqrt{3}}{5}, -\frac{2\sqrt{78}}{5}\right),\quad \left(-\frac{14\sqrt{3}}{5}, \frac{2\sqrt{78}}{5}\right),\quad \left(-\frac{14\sqrt{3}}{5}, -\frac{2\sqrt{78}}{5}\right) (5143,5278),(5143,−5278),(−5143,5278),(−5143,−5278)as shown in the diagram.
Find the equation of the circle C2C_2C2.
215 exam-style questions on Edexcel A Level Maths Parametric Equations, covering 8.1 Parametric Equations, 8.2 Using Trigonometric Identities, 8.3 Curve Sketching, 8.4 Points of Intersection, and 8.5 Modelling with Parametric Equations. Each one has a worked solution and a mark scheme showing where the marks go.