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Extra resources for An Introduction to Algebraical Geometry
Find the equation of a straight line through the intersection of 3#-f 5t/-7 = and 4#-f 6y-5 = parallel (i) to the axis of x, (ii) to the 18. axis of y. are that the two straight lines #-fy-fc = 0, \/3x + y-f d = inclined at an angle of 15. 20. Find the condition that the straight lines joining the origin to the points of intersection of the pairs of straight lines 19. Show to-f wr/ 0| should be (i) perpendicular, (ii) coincident. +1 = 0) THE EQUATION OF THE FIRST DEGREE 44 To find the coordinates of a point whose distance from a fixed and which lies on a straight line through (ex, ft) inclined 6.
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. Find the coordinates of a point which is equidistant from (a, b) and (2, Z>), and whose distance from the origin is -, 14.
Prove that /?. P, Q /*, Q 25 are (, 0), (b> 0), find those of OR internally and externally in the same ratio. 2 2 points whose coordinates are (aw 2am), (am~ divide P and Q are two and S is the point (a, 0). Prove (i) that PSQ arc collinear, is constant for all values of MI. (ii) 1/XP-f \/$Q 28. Choose the most convenient axes to represent the veitices of an equilateral triangle AB(' and find the coordinates of the centre (P) of its 27. ~ , , l ), t circumcircle. If Q is any point in the plane, find the ratio of 29.