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**Example text**

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. When one condition the line) Thus have if is we (e. g. a point on the line, or the direction of given, a relation between the constants can be found. >) lies on the straight line, we Aa + Bb + C = 0. THE EQUATION OF THE FIRST DEGREE 38 one of the independent terms of the other, and the equation of the line can be found in a form which involves only one unknown or It is then possible to find the value of ratios or constants in undetermined constant.

And we obtain M (+p)-2|Liy+jp-i. = the undetermined constant appears in the second degree. (A'x + Vy+V) = represents, for different values of ^ Q (i) a pencil of lines passing through and of the the point of intersection straight lines f / If we give jm increasingly large values, the A'x + y + C 0. Ax+Hy+C = = S straight line represented by (i) approaches the position of the straight It is sometimes said that for an infinite line A'x+By + C'= 0. It coincides with this straight line. correct, however, to write equation (i) in the form value of /JL it \(Ax + By+C) + n(A'x + B'y+C') is = safer and more Q.

T; , on 1 = ax -} (ii) meets tho by'+l. 23. If the sides of a parallelogram arc the straight lines u equation sides of a triangle arc of any point P(jt'\ 1 O (ae, (# cos #)/-{ (ysin0)/& is b'\ meet the straight (3, 2) to lines are bisected: lines w= 0, through the Find the equation of the straight line which joins the point of section of u = 0, v = 0, to that of u -f ic = 0, r + ww = 0. 24. inter- four sides of a quadrilateral have equations ui v = 0, r-i w> = 0, -u = 0, t;~ w = 0. Find the equations of its diagonals.