6 The line \(L\) has equation
$$5 y + 12 x = 298$$
A circle, \(C\), has centre \(( 7,9 )\)
\(L\) is a tangent to \(C\).
6
- Find the coordinates of the point of intersection of \(L\) and \(C\).
Fully justify your answer. - Find the equation of \(C\).
6
- Find the equation of \(C\).
\(7 \quad a\) and \(b\) are two positive irrational numbers.
The sum of \(a\) and \(b\) is rational.
The product of \(a\) and \(b\) is rational.
Caroline is trying to prove \(\frac { 1 } { a } + \frac { 1 } { b }\) is rational.
Here is her proof:
Step \(1 \quad \frac { 1 } { a } + \frac { 1 } { b } = \frac { 2 } { a + b }\)
Step 22 is rational and \(a + b\) is non-zero and rational.
Step 3 Therefore \(\frac { 2 } { a + b }\) is rational.
Step 4 Hence \(\frac { 1 } { a } + \frac { 1 } { b }\) is rational.