QJEEM19Ma3011: JEE Main 2019 Mathematics - Class 11 JEEM19Ma3011 Solution: If denotes the acute angle between the curves, y = 10 – x 2 and …

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 $\theta$ = $\left| {{{{m_1} - {m_2}} \over {1 + {m_1}{m_2}}}} \right|$

= $\left| {{{ - 4 - 4} \over {1 + \left( { - 16} \right)}}} \right|$

= ${8 \over {15}}$