By Alfred Clement Jones
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Extra info for An Introduction to Algebraical Geometry
Passes 8. r-7. 1; the equation of a straight line parallel to 2x + through the point (0, 4) (ii) through the origin ? is (a) (b) Some 3^/ = 6 which ; Find the angle between the pairs of 3. what angles do the the o:-axis ? y-4/S~x = lines 0, fSy-x = 0; y+y3# = 5, >v/3y-;r = 1. special forms of the equation of a straight line. Special attention should be paid to the results found for rectangular axes as before stated, oblique axes are not often necessary in the : more elementary parts of the subject.
THE EQUATION OF THE FIRST DEGREE ( 55 13. The algebraical sum of the perpendiculars from the points (xl} ;/ t ), X 2> Ui\ ( X ^y^> (#4> I/*) on a straight line is zero show that the line must pass : through the mean centre of the four points. Extend your proof to the case of any n fixed points. 14. A straight line is drawn through (5, 9) inclined at 45 to the axis of x. The straight line is cut in P, Show intersect at T. Q by x + 3y = 120, which pair the isosceles; give lengths of the equal PQT ia that = Ix + y 20, and the tangent of the angle at the veitex.
A i. straight line the straight line point Q. Find y = \/3# the length is to drawn through line, will illustrate the : we shall the point P('2, 3) parallel to meet the straight line 2x + iy = 27 in the PQ. r-axis straight line y of the equation straight line through (2, 3) parallel to it is The : hence the . , y) and the fixed point THE EQUATION OF THE FIRST DEGREE Now (2, 3). r-f ; r Hence 2 +4 2 r-f \ ^ J ^ / r+3 = hence - r is Ex. e. which 45 246, the required length of PQ. ii. To find the perpendicular distance Ax + By + C = the straight line of the point (a, I) from 0.
An Introduction to Algebraical Geometry by Alfred Clement Jones