# An Introduction to Algebraical Geometry by Alfred Clement Jones

By Alfred Clement Jones

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Additional info for An Introduction to Algebraical Geometry

Sample text

Special attention should be paid to the results found for rectangular axes as before stated, oblique axes are not often necessary in the : more elementary parts of the subject. The results are, however, worked out for future reference. for oblique axes THE EQUATION OF THE FIRST DEGREE 32, Form which it Tlie equation I. intercepts on Let the straight line that OA = a, straight line ; OB = its of the straight line in terms of the lengths the coordinate axes. 1. ' lii the making intercepts the equation of straight 1the axes is i# + # This result is true for rectangular and oblique axes.

3. Find the coordinates of the feet of the perpendiculars drawn from the point (1, 1) to the straight lines x-2 y + 2 = 0, Zx-y + \ = 0. Find also the length of the perpendicular drawn from the point (1, 1) to the the lines lines and 3#-4t/4l and find the straight line joining these feet. 4. Find the length of the perpendicular from the origin on (x cos6)/a 4 (y sin 6)/b 1. 5. Find the equations of the straight lines through the intersection of 6 == the straight lines 2,r 1/45 0, #4 3y respectively perpendicular and parallel to the straight line 5 #4 8//-10 = 0.

L of different sign. en is p, ^iiiLX, THE EQUATION OF THE FIRST DEGREE 48 of the perpendicular changes as the point P crosses the being of zero length when P is on the line. When dealing with more than one perpendicular we must call those drawn from points on one side of the line positive and those from points on the other negative. It follows similarly that all points whose The sign line, coordinates make Ax + By+G Ax + By + C~ 0, positive lie on one side of the line and those whose coordinates make Ax+By+C negative lie on the other side.