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1.3 Coordinate Geometry in the x-y Plane

1.3 Coordinate Geometry in the x-y Plane

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Question 21

A curve has the parametric equations

x=3sin⁡2θ,y=2cos⁡θ,0<θ<π x = 3\sin^2 \theta, \quad y = 2\cos \theta, \quad 0 < \theta < \pi x=3sin2θ,y=2cosθ,0<θ<π
a.

Find an expression for dydx\displaystyle \frac{dy}{dx}dxdy​ in terms of θ\thetaθ.

[3]
b.

Find an equation of the normal to the curve when θ=π3\displaystyle \theta = \frac{\pi}{3}θ=3π​.

[5]
c.

Find a cartesian equation for the curve.

[4]
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.

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