Question

Wyznacz m tak aby proste k i l były

a) równoległe

b)prostopadłe

k: y=2mx+2

l: y=(1-2m)x+6

Answer 1

a/  aby proste k: y=2mx+2  i  l: y=(1-2m)x+6  były równoległe

                                   a=a₁

                        gdzie a= 2m   a₁=1-2m

                                      2m=1-2m

                                      2m+2m=1

                                      4m=1

                                        m=1/4

            Proste k i l sa równoległe dla m=1/4

 

b/ aby w/w proste k i l były prostopadłe   a₁=-1/a

 

                                a=2m   a₁=1-2m

                              

                                  1-2m=-1/2m  |·2m

                                   2m(1-2m)=-1

                                   2m-4m²=-1

                                   -4m²+2m+1=0 |·-1

                                     4m²-2m-1=0

                                                        Δ=4-4·4·(-1)=4+16=20

                                                         √Δ=√20=2√5

                                  m₁=(2-2√5)/8 = (1-√5)/4

                                  m₂=(2+2√5)/8= ( 1+√5)/4

     proste k i l sa propstopadłe dla m₁= (1-√5)/2   i m₂=(1+√5)/2