Official solution
Angle between the curves is the acute angle between the tangents at the point of intersection.
y = 10 - x2 (for curve 1)
and y = 2 + x2 (for curve 2)
\[ \therefore \] 10 - x2 = 2 + x2
\[ \Rightarrow \] 2x2 = 8
\[ \Rightarrow \] x2 = 4
\[ \Rightarrow \] x = 2, - 2
\[ \therefore \] points of intersection (2, 6) and (- 2, 6)
\[{{dy} \over {dx}}\] for curve 1 = - 2x
\[ \therefore \] Slope(m1) of curve 1 is = - 2(2) = - 4
\[{{dy} \over {dx}}\] for curve 2 = 2x
\[ \therefore \] slope (m2) of curve 2 = 2 \[ \times \] 2 = 4
\[ \therefore \] tan\[\theta \] = \[\left| {{{{m_1} - {m_2}} \over {1 + {m_1}{m_2}}}} \right|\]
= \[\left| {{{ - 4 - 4} \over {1 + \left( { - 16} \right)}}} \right|\]
= \[{8 \over {15}}\]