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**Extra resources for An Introduction to Algebraical Geometry**

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And l- (a, b) a, b). ( What 23. >, the origin ? Write down an equation 24. moves lines so that the difference of its is by the coordinates of a point which distances from two intersecting straight satisfied constant. ) : if they are inclined at 30 trace the graph of 25. The polar coordinates of two points are (rlf 0^), through the pole bisecting the angle which they subtend their join in P. Find the polar coordinates of P. 26. , (r2 , tt 2) : the line at the pole Q from meets the origin form THE POINT a harmonic If the coordinates of series.

Example. lines (i) 3a? To find the in-centre + 40-12=0, (ii) of the triangle formed by the straight 5a-12y-20=0, (Hi) 24^-7^-72=0. 35 40 \ We see from the sides of the line and the origin are on opposite and hence the perpendiculars from these points must figure that the in-centre (i), be taken of opposite sign. r- 12 y y it same in-centre are on the = 20 negative, x x y , side of the line = \j (ii) : will therefore also x = 0, make negative. '-72) Hence the in-centre and the in-centre 1. is (4 = 1- 2 therefore - 5x' 4- 20).

R when = = = 3 and -3 respectively. What intercepts does each make when 18. 2 and a >rtan $7r4 c j:tan^7r ytan -'/TT 4c 4r 2 respectively. ; ; ; c Show on the axes? that the straight line x 4 // tan whatever value touches a fixed circle, 19. If the straight lines # ft = 8 ^ = a have. may 3x + my + l 3wy-9o;-f 3 sec 0, 0, are perpendicular, find the value of m. 20. Find the equation of the straight line perpendicular to which (i) (ii) (iii) cuts off a length 4 units frcffn the #-axis 4 units from the y-axis cuts off is distant 5 units from the origin.