F.4 Maths

1a)
For the curve cuts A,B two points, a and b are the roots of the equation.
sum of roots = a+b = -(-p)/1 = p
given AB = 6 => b-a = 6
product of roots = ab = 4
on solving, a= -3±√13 b= 3±√13 ( for b>a>0 )
so a =-3+√13 b = 3+√13
so p= 2√13

1b) For symmetric the axis of symmetry : x = (a+b) / 2 = p/2 = √13

2)
8^(x/3)=16^(y+2) -------1
2^(x-1)-3^2y=0 -------2

<1> : 2^x = 2^(4y+8) so x=4y+8
<2> : 2^(4y+7)=3^2y

y= 7/(2ln3/ln4 - 4) x = 7/(ln3/ln2 - 2)