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The equations of two circles S, and S, are given by S²+²+2x+2y+1=0. S: x + y²-4x+2y +1 -0. Show that S. and S, touch each other externally and obtain the equation of the common tangent 7 at the point of contact.

The equations of two circles S, and S, are given by S²+²+2x+2y+1=0. S: x + y²-4x+2y +1 -0. Show that S. and S, touch each other externally and obtain the equation of the common tangent 7 at the point of contact.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.2: Direct Methods For Solving Linear Systems
Problem 3CEXP
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8 I ( 9 O 0 P 712 ( [ + End 1 1 7. () Find all the values of 8, oss, for which 20 () Show that the matris M is invertible, where -25 M- 9 Hence, find M, the inverse of matrix M. 10. (i) Given that 47/0765/2/C/Q Insert 4 8( & Given that )= (1+30)=1-27, express the complex number in the form w+, where and t are real constants. () (i) The vector equation of two lines L, and L, are given by y= Delete Backspace Find (a) the position vector of the point of intersection of L, and L (b) the cosine of the acute angle between L., and 42- 4₁=131+41+11k+2031-81-60). 9. (i) The equations of two circles Si and S, are given by S₁x² + y² + 2x +2y+1=0. L₂=51+221 +9k+(71-171-5k). S₂x² + y²-4x+2y+1 -0. Show that S. and S touch each other externally and obtain the equation of the common tangent T at the point of contact. (i) A father and a mother have 5 children. This family is to occupy a particular front-line bench in church on a special thanksgiving service. Given that this bench has a capacity of 7 persons, in how many ways can this family be seated on the bench (a) if the parents must sit adjacent to each other.. (b) if the parents must sit adjacent to each other at one end of the bench. 2 f(x)= x(x + 1)(x + 2) express f(x) in partial fractions. Hence show that f(x) dx = In () (ii) Sketch the graph of the curve whose equation is given by 2x - 7 x-4 showing clearly the points where the curve meets the coordinate axes and the behavior of the curve near its asymptotes. (x+2)+c-b 39 (3+244-4
Transcribed Image Text:8 I ( 9 O 0 P 712 ( [ + End 1 1 7. () Find all the values of 8, oss, for which 20 () Show that the matris M is invertible, where -25 M- 9 Hence, find M, the inverse of matrix M. 10. (i) Given that 47/0765/2/C/Q Insert 4 8( & Given that )= (1+30)=1-27, express the complex number in the form w+, where and t are real constants. () (i) The vector equation of two lines L, and L, are given by y= Delete Backspace Find (a) the position vector of the point of intersection of L, and L (b) the cosine of the acute angle between L., and 42- 4₁=131+41+11k+2031-81-60). 9. (i) The equations of two circles Si and S, are given by S₁x² + y² + 2x +2y+1=0. L₂=51+221 +9k+(71-171-5k). S₂x² + y²-4x+2y+1 -0. Show that S. and S touch each other externally and obtain the equation of the common tangent T at the point of contact. (i) A father and a mother have 5 children. This family is to occupy a particular front-line bench in church on a special thanksgiving service. Given that this bench has a capacity of 7 persons, in how many ways can this family be seated on the bench (a) if the parents must sit adjacent to each other.. (b) if the parents must sit adjacent to each other at one end of the bench. 2 f(x)= x(x + 1)(x + 2) express f(x) in partial fractions. Hence show that f(x) dx = In () (ii) Sketch the graph of the curve whose equation is given by 2x - 7 x-4 showing clearly the points where the curve meets the coordinate axes and the behavior of the curve near its asymptotes. (x+2)+c-b 39 (3+244-4
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