WELCOME TO THE HIGHER MATHEMATICS CLASS SHIPAN CHANDRA DEBNATH ASSISTANT PROFESSOR & HEAD OF THE DEPARTMENT DEPARTMENT OF MATHEMATICS CHITTAGONG CANTONMENT PUBLIC COLLEGE scnctg@gmail.com

THE STRAIGHT LINES Chapter - 3 Exercise -3(F) Book: Higher Mathematics Akkhar-patra Publications

Learning Outcomes After complete this chapter students can Explain parallelism of two straight lines 2. Explain perpendicularity of two straight lines

1.Condition of parallelism: If the Lines a1x+b1y+c1=0 & a2x+b2y+c2=0 are parallel then slopes are equal i.e m1=m2 or, a1b2=a2b1 2.Condition of perpendicularity: If the Lines a1x+b1y+c1=0 & a2x+b2y+c2=0 are perpendicular then product of two slopes equal to -1 i.e m1m2=-1or a1a2+b1b2=0 3. The parallel equation of the line ax+by+c=0 is ax+by+k=0 4. The perpendicular equation of the line ax+by+c=0 is bx-ay+k=0

5. If the Lines a1x+b1y+c1=0 ,a2x+b2y+c2=0 & a3x+b3y+c3=0 are concurrent then

CLASS WORK 1.Show that the Straight lines 10x+11y+12=0 and 10x+11y-13=0 are parallel. 2.For what value of k the lines 5x+4y+6=0 and 3kx-4y-2=0 are perpendicular?. 3.Find the equation of the Straight line which is parallel to the line 2x-3y+4=0 and passes through the point (-2,-3) 4. Find the equation of the Straight line which is perpendicular to the line 2x-3y+4=0 and passes through the point (-2,-3)

EVALUATION what is the condition of perpendicularity? what is the condition of parallelism?

HOME WORK Find the equation of the Straight line which is perpendicular to the line 2y=11x+7 and passes through the point (-2,-3) Two Straight lines passes through the point (3,2) & makes angle 450 with the Straight line x-2y-3=0, Find their equation. Find the equation of the Straight line which is parallel to the line 2x+11y-2=0 and passes through the point (-1,3) .

THANKS TO ALL EUCLID, Father of Geometry