June 2017 Paper 1 Q10
10 Circle C\(_1\) has centre \(L\) and equation \(\quad (x - 3)^2 + y^2 = 36\)
Circle C\(_2\) has centre \(M\) and equation \(\quad (x - h)^2 + y^2 = 64 \quad\) where \(h\) is a constant.
The circles intersect at \(N\).
\(LN\) is perpendicular to \(MN\).
Not drawn accurately
Work out the value of \(h\). [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| (3, 0) marked or used | B1 | |
| radii 6 and 8 identified | B1 | oe |
| \(\sqrt{(6^2 + 8^2)}\) or 6, 8, 10 triangle or 10 | M1 | |
| (\(h\) =) 13 or M = (13, 0) | A1 | might be seen in the working or on the diagram |
Additional guidance
(3, 0) can be implied eg \(LM = h - 3\) or \(OM = 3 +\) their \(LM\)
Look on the diagram for evidence of the B marks
(\(h\) =) 13 with no working is 4 marks (\(-13\) with no working is 0 marks)