By V. I ArnolÊ¹d

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J^cos ^ ; line, ( /) (ji) + 7) =. 0, 7) 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.

What equation is by coordinates of satisfied this form, a, 7>, and r being fixed? Show that the 17. is the same for Draw 18. all distance between the points {-f5,& + 9], {a 4 and b. Find the distance. the graphs of xy ^xy + if + rcoa(0 + JTT) = x^ (i) (ii) 19. 2, ft-f 5] values of a ; 2. The coordinates of three points AJ^ Care (8, 6), (7, 7), (0,6); show that they are equidistant from the point (4, B). Find an equation satisfied by the coordinates of any point on the circle ABC. 2 20. Find the distance of the point (a tan 0, 20tan0) from (, 0), and from = x 0.

If u = 0, v = represent two straight lines, any line through their point of intersection If u' EE (#', y'} Ax' + By' + should interpret v f lie = C, is u + \v then w' = = 0. is the condition that the point on the straight line u = ; and similarly we 0. + Xv = passes through some given point u'v At/ 0, hence w/ represents the straight (#'> y'\ then tt'-f 0, line joining the point (/, y') to the intersection of u 0, v r a w line represents straight through (/, y'} parallel Again, u If the straight line u = = = = = to u = 0.