5. The hyperbola \(H\) has equation \(\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 4 } = 1\)
The line \(l\) has equation \(y = m x + c\), where \(m\) and \(c\) are constants.
Given that \(l\) is a tangent to \(H\),
- show that \(25 m ^ { 2 } = 4 + c ^ { 2 }\)
- Hence find the equations of the tangents to \(H\) that pass through the point ( 1,2 ).
- Find the coordinates of the point of contact each of these tangents makes with \(H\).