If P and the origin are the points of intersection of the parabolas y^2=32 x and 2 x^2=27 y ; and if is the acute angle between these curves at P , then 5 =

Step-by-step solution

Points of intersection of curves From Eqs. (i), and (ii), we get aligned 2 ( y^2 32 )^2 & =27 y 2 y^4 & =27 32 32 y y & =0, y^3=512 27 y & =24 aligned From Eq. (i), we get aligned & x=0 & x=18 aligned So, coordinate of P(18,24) . Equation of tangent through point P(18,24) on the curve y^2=32 x aligned & y 24=16(x+18) & 3 y=2 x+36 & Slope m₁=2 / 3 & aligned Again equation of tangent through point P(18,24) on the 2 x^2=27 y aligned & 2 x 18 & =27 (y+24) 2 & & 8 x=3 y+72 & 3 y & =8 x-72 aligned Slope, m₂=8 / 3 Angle b