By Alfred Clement Jones
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Extra info for An Introduction to Algebraical Geometry
R+my+n = fo'+ 0, (i) 0, (ii) #+w = (iii) represents a straight line and contains two independent constants. No one of them, however, is suitable for a general discussion the first cannot represent a straight line through the origin, the second ; cannot represent a straight line parallel to the axis of #, the third cannot represent a straight line parallel to the axis of //. It is evident then that two conditions are necessary to fix a and further that in the cases above given these two conditions are sufficient: we shall see later that two conditions are straight line, not always sufficient.
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. Prove that /?. P, Q /*, Q 25 are (, 0), (b> 0), find those of OR internally and externally in the same ratio. 2 2 points whose coordinates are (aw 2am), (am~ divide P and Q are two and S is the point (a, 0).
General propeity can you deduce from this result ? show that D, a point of trisection of AC 57. ABCD is a parallelogram axis of What : and the mid-point of AB, are The 58. vertices &sin0-f $7r), of (acostf-f $TT, a collinear. triangle frsin = 0+ are TT). (acos#, (i) Prove 5sin0), its centroid is the origin. show that the triangle is equilateral. Find its area, (iii) If a (ii) 21 has its ends on the axes of reference: 59. A straight line of length find the equation of the locus of its middle point.
An Introduction to Algebraical Geometry by Alfred Clement Jones