The curve C1 C_1\,C1 has parametric equations
x=6costx = 6\cos tx=6cost, y=25sinty = 2\sqrt{5}\sin ty=25sint, where 0≤t<2π0 \leq t < 2\pi0≤t<2π
C1 C_1\,C1 meets the circle C2C_2C2, which has equation x2+y2=25x^2 + y^2 = 25x2+y2=25, at four distinct points, as shown in Figure 1 below.
Find the exact Cartesian coordinates of the four points of intersection.
143 exam-style questions on OCR A Level Maths 1.3 Coordinate Geometry in the x-y Plane, covering 1.3.1 Straight lines, 1.3.2 Parallel and perpendicular lines, 1.3.3 Straight line models, 1.3.4 Coordinate geometry of a circle, 1.3.5 Centre and radius by completing the square, 1.3.6 Circle properties, 1.3.7 Parametric equations of curves (A-level only), 1.3.8 Parametric equations in context (A-level only), and 1.3 Coordinate Geometry in the x-y Plane. Each one has a worked solution and a mark scheme showing where the marks go.