*7-8.) in './// l.i.Vg 



8. 4 -r 1 - 1'Jry + Of - Jrx + fljr + 1 0. 



9. The equationi of the opposite sides of a parallelogram are 



quations of the diagonals. 



10. 1 u.l the conditions that Uie airtight lines represented by the eqoa- 

 '9 + Cy a may be real ; imaginary; coincident; perpen- 

 dicular to each other. 



1 1 Show that x + 5iy - fly* = M the equation of the bisectors of 

 the angles made by the linen ry + 7 y* = o. Doss the first set 



..f line* fulfil the u*l of exercise 10 for perpendicularity 7 



6a Equations of straight lines: coordinate axes oblique. 



in th. ion of equations ['.] and [10] (Art* 



and 52) only properties of similar triangles were employed, 

 therefore these two equations are true whether the coordi- 

 nate axes are rectangular or oblique. 



The other three standard forms however, viz. y asm* + 6, 

 y jf|BBin( Xj ).aml f cos a +y sin a =/>, the derivation of 

 which depends upon riiht mangles, are no longer true if 

 the axes are incline* 1 to each other at an angle =* j- Equa- 



I which correspond to these, but \\hich are referred to 

 oblique axes, will now be derived. 



(1) Equation of ttrnijht Urn- throw/h a given point and in 



l 



Inn- 



fixed point P^^r^y^ and 

 making an angle with th.- 

 XIH, let Ps (x, y) be any 



int mi LL V and let 



e 1)6 the angle between tin- 



Draw P l R parallel to th. 



also draw th- m-di nates Af,P, and MP. 



and 



T 



