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`(7)/(17)` `(8)/(15)``(4)/(9)` `(8)/(17)`

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BSolution :

Given equation of curves are <br> `" " y = 10 - x ^(2)" " `…(i) <br> and `" " y = 2 + x^(2)" " ` … (ii) <br> For point of intersection, consider <br> `" " 10- x^(2) = 2 + x ^(2)` <br> `rArr " " 2x^(2) = 8` <br> `rArr " "x ^(2) = 4` <br> `rArr " " x= pm 2 ` <br> Clearly, when `x =2` , then `y =6` (using Eq. (i)) and when `x = - 2` , then `y = 6` <br> Thus, the point of intersection are `(2, 6) and (-2, 6)`. <br> Let `m_1` be the slope of tangent to the curve (i) and `m_2` be the slope of tangent to the curve (ii) <br> For curve (i) `(dy)/(dx) = -2 x and ` for curve (ii) `(dy)/(dx)= 2x` <br> `therefore ` At ` (2, 6)`, slope `m_1 =-4 and m_2=-4` and in that case <br> `|tan theta| = |(m_2 - m_1)/(1+ m_1m_2)| = | (-4 -4)/( 1-16)| = (8)/(15)` <br> At `(- 2, 6)`, slopes `m_1 = 4 and m_2 = - 4 ` and in that case <br> `|tan theta| = |(m_2 - m_1)/(1+m_1m_2)| = |(-4-4)/(1-16)|= (8)/(15)`