CirclesEdexcel A-Level Maths: Subtopic test

1. 1
   A circle $C$ has equation $x^2+y^2-6x+4y-12=0$.

   (a)

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

   [1 mark]

   • A$(-3,2)$
   • B$(3,-2)$
   • C$(6,-4)$
   • D$(-6,4)$

   (b)

   Find the radius of $C$.

   [1 mark]

   • A$\sqrt{12}$
   • B$25$
   • C$\sqrt{21}$
   • D$5$

   (c)

   Determine whether the point $(6,3)$ lies inside, outside or on $C$. Show your working.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A circle has centre $C(2,1)$ and passes through the point $A(5,5)$.

   (a)

   Find the radius of the circle.

   [1 mark]

   • A$5$
   • B$25$
   • C$7$
   • D$\sqrt7$

   (b)

   Find the gradient of the tangent to the circle at $A$.

   [1 mark]

   • A$\frac43$
   • B$\frac34$
   • C$-\frac34$
   • D$-\frac43$

   (c)

   Find the equation of the tangent to the circle at $A$, giving your answer in the form $ax+by+c=0$, where $a$, $b$ and $c$ are integers.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   The points $A(-1,2)$ and $B(5,10)$ are the endpoints of a diameter of a circle $S$.

   (a)

   Find the equation of $S$.

   [3 marks]

   (b)

   Show that the point $D(6,3)$ lies on $S$ and that angle $ADB$ is a right angle.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   Triangle $PQR$ has vertices $P(0,6)$, $Q(7,5)$ and $R(6,-2)$.

   (a)

   Find the equation of the circle that passes through $P$, $Q$ and $R$, giving your answer in the form $(x-a)^2+(y-b)^2=r^2$.

   [6 marks]

   (b)

   The circumcircle of triangle $PQR$ has centre $C(3,2)$ and radius $5$. The tangent to the circumcircle at $P$ meets the $x$-axis at $T$. Find the area of triangle $CPT$.

   [6 marks]

   Total for question 4: 12 marks

End of questions