Skip to content

Course home

1.3 Coordinate Geometry in the x-y Plane

1.3 Coordinate Geometry in the x-y Plane

EasyMediumHard
1234567891011121314151617181920212223
Question 14

The curve C C\,C has parametric equations

x=3cos⁡θx = 3\cos\thetax=3cosθ, y=2sin⁡θy = 2\sin\thetay=2sinθ, where 0≤θ<2π0 \leq \theta < 2\pi0≤θ<2π

a.

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​.

[2]
b.

Show that the tangent to C C\,C at P P\,P has equation

2x+33y=122x + 3\sqrt{3}y = 122x+33​y=12

[5]
Markscheme

1.3 Coordinate Geometry in the x-y Plane Questions

  1. A Level
  2. /Maths
  3. /1.3 Coordinate Geometry in the x-y Plane

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.

Question bank