Parametric equationsEdexcel A-Level Maths: Subtopic test

1. 1
   A curve $C$ has parametric equations $x=2t+1$, $y=4t^2-3$, where $t$ is a real number.

   (a)

   Find the coordinates of the point on $C$ where $t=2$.

   [1 mark]

   • A$(5,16)$
   • B$(4,13)$
   • C$(5,13)$
   • D$(5,5)$

   (b)

   Find a Cartesian equation of $C$.

   [1 mark]

   • A$y=x^2-2x-2$
   • B$y=4x^2-3$
   • C$y=x^2-2x+1$
   • D$y=x^2+2x-2$

   (c)

   Find the coordinates of the point where $C$ crosses the $y$-axis.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A curve $D$ has parametric equations $x=-2+4\cos t$, $y=3+4\sin t$, for $0\le t<2\pi$.

   (a)

   Write down the coordinates of the centre of $D$.

   [1 mark]

   • A$(2,-3)$
   • B$(-2,3)$
   • C$(4,4)$
   • D$(-2,-3)$

   (b)

   Find a Cartesian equation of $D$.

   [1 mark]

   • A$(x-2)^2+(y+3)^2=16$
   • B$(x+2)^2+(y-3)^2=4$
   • C$x^2+y^2=16$
   • D$(x+2)^2+(y-3)^2=16$

   (c)

   Find the values of $t$, for $0\le t<2\pi$, at the points where $D$ meets the line $x=0$.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A curve $H$ has parametric equations $x=3t$, $y=\frac{12}{t}$, where $t\ne0$.

   (a)

   Find a Cartesian equation of $H$ in the form $xy=k$, and state the values that $x$ cannot take.

   [3 marks]

   (b)

   The line $x+y=15$ meets $H$ at two points. Find the coordinates of these points.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A curve $S$ has parametric equations $x=2+4\cos t$, $y=-1+4\sin t$, for $0\le t\le\pi$.

   (a)

   (i) Find a Cartesian equation of $S$.
   (ii) Describe the curve $S$, including which part of the circle it is.

   [6 marks]

   (b)

   The curve $S$ meets the line $y=1$ at two points. Find the exact distance between these two points.

   [6 marks]

   Total for question 4: 12 marks

End of questions