MAT 121 Lecture : Analytical geometry - MAT 103 -Pairs of Lines
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We solve this equation by the general law we obtain passes through the origin. The homogenous equation of second degree: this equation is the equation which its all non-zero terms are of second degree where (cid:1853)(cid:1876)(cid:2870)(cid:3397)(cid:884)(cid:1860)(cid:1876)(cid:1877)(cid:3397)(cid:1854)(cid:1877)(cid:2870)(cid:3404)(cid:882) ((cid:883)) This equation can be written as equation of second degree in (cid:1877) as (cid:1854)(cid:1877)(cid:2870)(cid:3397)((cid:884)(cid:1860)(cid:1876))(cid:1877)(cid:3397)(cid:1853)(cid:1876)(cid:2870)(cid:3404)(cid:882) (cid:1877)(cid:3404)(cid:3398)(cid:884)(cid:1860)(cid:1876)(cid:3399)(cid:3493)((cid:884)(cid:1860)(cid:1876))(cid:2870)(cid:3398)(cid:886)(cid:1853)(cid:1854)(cid:1876)(cid:2870) (cid:884)(cid:1854) (cid:1877)(cid:3404)(cid:3398)(cid:1860)(cid:3399) (cid:1860)(cid:2870)(cid:3398)(cid:1853)(cid:1854) (cid:1876) ((cid:884)) (cid:1854) The two equations in ((cid:884)) represent two straight lines which passes through the origin so the homogenous equation of second degree in ((cid:883)) represent two straight lines which. The two straight lines in ((cid:884)) are : Find the equations of these two straight lines (cid:890)(cid:1876)(cid:2870)(cid:3398)(cid:888)(cid:1876)(cid:1877)(cid:3397)(cid:1877)(cid:2870)(cid:3404)(cid:882). Then the two straight lines are (cid:1877)(cid:3404)(cid:884)(cid:1876) (cid:481) (cid:1877)(cid:3404)(cid:886)(cid:1876) . Assume that the two lines which represent in ((cid:883)) are (cid:1877)(cid:3404)(cid:1865)(cid:2869)(cid:1876) (cid:481) (cid:1877)(cid:3404)(cid:1865)(cid:2870)(cid:1876) The angle between the two straight lines which represent by the homogenous equation. Where (cid:1865)(cid:2869) (cid:481)(cid:1865)(cid:2870) the gradient of these two lines so ((cid:1877)(cid:3398)(cid:1865)(cid:2869)(cid:1876))((cid:1877)(cid:3398)(cid:1865)(cid:2870)(cid:1876))(cid:3404)(cid:882) (cid:1525) (cid:1877)(cid:2870)(cid:3398)((cid:1865)(cid:2869)(cid:3397)(cid:1865)(cid:2870))(cid:1876)(cid:1877)(cid:3397)(cid:1865)(cid:2869)(cid:1865)(cid:2870)(cid:1876)(cid:2870)(cid:3404)(cid:882) ((cid:885))
