By Alfred Clement Jones
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Extra info for An Introduction to Algebraical Geometry
Flic equation of the straight line in and the angle pendicular on it from the origin x-axis. ) 10 Let the length of the perpendicular be p and the angle made by it with the x-axis be ex. This angle must be measured from Ox as THE EQUATION OF THE FIRST DEGREE initial line as in polar coordinates 33 thus the polar coordinates of the : foot of the perpendicular on the straight line are (p, OK). and J2. Letjiue^traight line meet the axes in A OA p sec a, OB = JM cpsec Hence == ex. Therefoie by the equation (i) x cos to # sin y.
THE POINT 24 Find the cosine of the angle which the straight line joining the points b\ (a', I') subtends at the origin. 9. (a, 10. The coordinate axes being inclined at 60, prove that (a, 0), (0, 2r<), an equilateral triangle. 11. The centre of a circle is (3, 5), one end of a diameter is (7, 3) what are the coordinates of the other end of this diameter ? Find the radius. 12. Prove analytically that the three straight lines joining the vertices of (2 a, a] are the corners of ; a triangle to the mid-points of the opposite sides have one point of trisection in common.
30. Show that the points (a, a), (fc, Av/) subtend a right angle at the Prove also that the triangle whose vertices are (3, origin. 2), ( 5, + 4), (9, G) is right-angled. + atan 2 0, 2 a tan 0) is equally distant from the ( and axis the of point (2fl, 0), y for all values of 0. 32. Show that the middle points of the non-parallel sides of a trapezium and the middle points of its diagonals lie on a straight line parallel to the Prove that the point 31. parallel sides. Find the equation of tho locus of a point P which moves so that the tin* rectangle formed by the axes and the perpendiculars from P 33.