By Alfred Clement Jones

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**Extra info for An Introduction to Algebraical Geometry**

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Find the condition that the coordinates of the middle point of the 35. 3c. straight line joining (a, />), (26, 2 a) should satisfy the equation 2x + 30. Find the equation of the locus of the middle point of straight lines drawn from a given point to any point in a given straight line. 2y= In any triangle 2 2 37. that A B + A G* = ABC, if AD + 2 BD 2 D is the mid-point of BC, prove analytically 2 . <), and hence prove 38. + CA* = 3 (AG* + <7 2 -f CG 2 ). 39. The sum of the squares on the diagonals of any quadrilateral is double the sum of the squares on the lines joining the middle points of the opposite sides.

V) Find the coordinates of the points on oach of these straight lines whose abscissae are 10, and prove that these points form another harmonic range. 50. ( r i Find the condition that the three points whose polar coordinates are (*a ^a)> ( rs ^s) should be collinear. ^i) 51. Find the ratio of the areas of t,wo triangles whoso angular points are 2 (i) (ii) (a\ ,2a\), {aX/u, a 52. Express algebraically that the distance of the point (x, y) is What is (3, 4) the graph of the equation ? A, B are fixed points on the axes find the equation of the locus of point P such that 2 OP = AP* 4 BP given that OA = a, OB = b.

Z = 21. 6. Find the equation of the straight line drawn through the point (x^ y^ perpendicular to the straight line joining the points (a" 2 ,y 2 ), ^3 Va)7. Find the equation of a straight line passing through the intersection of which is parallel to px + qy + r = 0. cur 4 by -i c = 0, ax -f b'y -f c = 8. What the length of the =2? is perpendicular from the origin on the 3# + 4y straight line Find the tangent of the angle this perpendicular makes with the axis of x. The centre of an equilateral triangle is at the origin, and one side of the = 2.