By Alfred Clement Jones

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Extra info for An Introduction to Algebraical Geometry

Example text

Prove that /?. P, Q /*, Q 25 are ( 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.

2 =^0, a^x + the four points are given by the equation _ ~~ To determine example in any special case which solution corresponds for to the in-centre. the student should draw the graph of the lines. Example. lines (i) 3a? To find the in-centre + 40-12=0, (ii) of the triangle formed by the straight 5a-12y-20=0, (Hi) 24^-7^-72=0. 35 40 \ We see from the sides of the line and the origin are on opposite and hence the perpendiculars from these points must figure that the in-centre (i), be taken of opposite sign.

A 60. and b its x+ v/ 3y-~2r=0, : Find the distance between two points whose polar coordinates are 61. (6,iir),(-3, ITT). 62. P is a point inside a parallelogram ABCD such that the area double the area PBAD: find the equation of the locus of P. PBCD is A point moves so that the ratio of its distances from the points 2 3 find the equation of its locus. Where docs the locus meet the axis of x ? 63. (-, 0), (a, 0) is 64. (*, y n ). is bisected at (ar 2 , t/ 2 ), t/ 3 ) AB divided at so that P3 (n- 1) so P,Cis divided at P2 so that 2PjP2 = P2 C, P2 Z) is that 3PoP3 = Pn D, and so on until Pn ^K is divided at Pn _, P,, Pn _^Vi = pn -i K - Find the coordinates of PM-1 .