Edexcel PMT Mocks — Question 6

Exam BoardEdexcel
ModulePMT Mocks (PMT Mocks)
TopicCircles

6. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{63d85737-99d4-4916-a479-fe44f77b1505-10_951_1022_306_488} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} The circle \(C\) has centre \(A\) with coordinates \(( - 3,1 )\).
The line \(l _ { 1 }\) with equation \(y = - 4 x + 6\), is the tangent to \(C\) at the point \(Q\), as shown in Figure 3.
a. Find the equation of the line \(A Q\) in the form \(a x + b y = c\).
b. Show that the equation of the circle \(C\) is \(( x + 3 ) ^ { 2 } + ( y - 1 ) ^ { 2 } = 17\) The line \(l _ { 2 }\) with equation \(y = - 4 x + k , k \neq 6\), is also a tangent to \(C\).
c. Find the value of the constant \(k\).