9 Given that 2x +ty 4t is a tangent to the rectangular hyperbola xy = 4 at the point P (2t,-), find the real value(s) of 2. The tangent meet the x-azis at A and y - azis at B. The line through A...

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Extracted text: 9 Given that 2x +ty 4t is a tangent to the rectangular hyperbola xy = 4 at the point P (2t,-), find the real value(s) of 2. The tangent meet the x-azis at A and y - azis at B. The line through A parallel to the y- axis meets the hyperbola at C, while the line through B parallel to the z – axis meets the hyperbola at D. Show that as P varies, the locus of the midpoint of CD is the perpendicular hyperbola 4xy = 25 10. (a) The figure shows a square lamina of side a with its vertex inclined at an angle 0,0 SOS pla a line AB, A. Show that the centre of the lamina is at a distance sin (9+) from AB. 2. The lamina is rotated completely about the lipe AB, shows that the volume of the solid generated is VZna? sin (9+) (b) Find the greatest common divisor (gcd), t, of 427 and 1037. Hence find the integers and such that 427r+1037s =t. Deduce that 7r+ 17s FORAM MEAFO STRVE ANO THE PREPARING EXCELLENCE SER