(a)[2]
Find the equation for the tangent $CBD$.
(b)[3]
Find an equation for the circle centred at $B$.
(c)[3]
By calculation, find the $x$-coordinates of $C$ and $D$.
Mathematics 9709 · AS & A Level · Coordinate geometry
Coordinate geometry — practice question
The diagram depicts a circle with centre $A$ that passes through $B$. A second circle is centred at $B$ and passes through $A$. The tangent at $B$ to the first circle cuts the second circle at $C$ and $D$. The coordinates of $A$ are $(-1, 4)$ and the coordinates of $B$ are $(3, 2)$.