Question 6 - A-Level Maths

6. A curve has equation $x ^ { 2 } + y ^ { 2 } + 12 x = 64$
A line has equation $y = m x + 10$

1. In the case that the line intersects the curve at two distinct points, show that $$( 20 m + 12 ) ^ { 2 } - 144 \left( m ^ { 2 } + 1 \right) > 0$$
(ii) Hence find the possible values of $m$.
1. On the same diagram, sketch the curve and the line in the case when $m = 0$
(ii) State the relationship between the curve and the line.