The curve C C\,C has parametric equations
x=3cosθx = 3\cos\thetax=3cosθ, y=2sinθy = 2\sin\thetay=2sinθ, where 0≤θ<2π0 \leq \theta < 2\pi0≤θ<2π
Show that a Cartesian equation for C C\,C is x29+y24=1\dfrac{x^2}{9} + \dfrac{y^2}{4} = 19x2+4y2=1.
The point P P\,P on C C\,C has parameter θ=π3\displaystyle \theta = \frac{\pi}{3}θ=3π.
Show that the tangent to C C\,C at P P\,P has equation
2x+33y=122x + 3\sqrt{3}y = 122x+33y=12
178 exam-style questions on OCR (MEI) A Level Maths 1.5 Coordinate Geometry, covering 1.5.1 Equation of a straight line y = mx + c, 1.5.2 Gradients of parallel and perpendicular lines, 1.5.3 Distance between two points, 1.5.4 Midpoint of a line segment, 1.5.5 Form the equation of a straight line, 1.5.6 Draw a line given its equation, 1.5.7 Point of intersection of two lines, 1.5.8 Straight line models, 1.5.9 Intersection of a line and a curve, 1.5.10 Intersection of a line and a circle, 1.5.11 Equation of a circle, 1.5.12 Circle properties, 1.5.13 Parameter and parametric equations (A-level only), 1.5.14 Convert between cartesian and parametric forms (A-level only), 1.5.15 Equation of a circle in parametric form (A-level only), 1.5.16 Gradient of a parametric curve (A-level only), 1.5.17 Parametric equations in modelling (A-level only), and 1.5 Coordinate Geometry. Each one has a worked solution and a mark scheme showing where the marks go.