Equation of a circleEdexcel International A Level Maths: Subtopic test

1. 1
   A circle has equation $(x-3)^2+(y+2)^2=25$.

   (a)

   Write down the coordinates of the centre of the circle.

   [1 mark]

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

   (b)

   Write down the radius of the circle.

   [1 mark]

   • A$25$
   • B$\sqrt5$
   • C$12.5$
   • D$5$

   (c)

   Determine whether the point $(6,2)$ lies inside, outside or on the circle.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A circle has centre $(-4,1)$ and passes through the point $(-2,4)$.

   (a)

   Which of the following is the equation of the circle?

   [1 mark]

   • A$(x-4)^2+(y+1)^2=13$
   • B$(x+4)^2+(y-1)^2=\sqrt{13}$
   • C$(x+4)^2+(y-1)^2=13$
   • D$(x+4)^2+(y-1)^2=5$

   (b)

   What is the greatest value of $y$ on the circle?

   [1 mark]

   • A$1+\sqrt{13}$
   • B$4$
   • C$\sqrt{13}$
   • D$14$

   (c)

   Find the coordinates of the points where the circle meets the line $y=1$.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A circle $C$ has equation $x^2+y^2-10x+4y+13=0$.

   (a)

   Find the coordinates of the centre of $C$ and the radius of $C$.

   [3 marks]

   (b)

   Find the exact $x$-coordinates of the points where $C$ meets the $x$-axis.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   The line segment $AB$ is a diameter of a circle $C$, where $A$ is the point $(-3,1)$ and $B$ is the point $(5,5)$.

   (a)

   Find the equation of $C$, and show that the point $P(5,1)$ lies on $C$.

   [6 marks]

   (b)

   The circle $C$ meets the $y$-axis at two points. (i) Find the exact $y$-coordinates of these points. (ii) Find the exact distance between the two points. (iii) Determine whether the origin lies inside the circle.

   [6 marks]

   Total for question 4: 12 marks

End of questions