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1.5.14 Convert between cartesian and parametric forms (A-level only)

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Question 20

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]

1.5.14 Convert between cartesian and parametric forms (A-level only) Questions

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