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Answer question 10b showing fully all the steps. Solution should be simplified and easy to undertand as much as possible!

Answer question 10b showing fully all the steps. Solution should be simplified and easy to undertand as much as possible!

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.3: Hyperbolas
Problem 35E
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Answer question 10b showing fully all the steps. Solution should be simplified and easy to undertand as much as possible!

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
Transcribed Image 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
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