Question

(P): y= -1/2x²

(d): y= x-3/2

(d'): y= mx+1/2

A, Tim giao diem ua (P) va (d) bang hai cach.

B, tim m de (d') tiep xuc voi (p)

C, tim m de (d') tiep xuc voi (p) va vuong goc voi (d)

Answer 1

(P): y= -1/2x²

(d): y= x-3/2

(d'): y= mx+1/2

xet’ PTHDGD ca (P) & (d)

 -1/2x²  = x-3/2

=>  -1/2x²  - x + 3/2 = 0

=> x = 1 ; x = 3

Thay x = 1 ; x = 3 vao (P)

=>y = -1/2 .1² = -1/2 ; y   = -1/2 .(-3) ² = -9/2

Vay giao diem cua   (P) & (d) la (1 ; -1/2 ) (3 ; -9/2)

b.xet PTHDGD cua (P) & (d’)

mx+1/2 = -1/2x²   

1/2x²   - mx -1/2 = 0

Δ = b²  - 4ac = (-m) ²  - 4.\(\frac{1}{2}\)\(\frac{1}{2}\) =m ²  - 1

De (P) txuc vs (d’) <=> Δ = 0 <=> m ²  - 1 = 0

                                              <=>m = ± \(\sqrt{ }\)1

hinh nhu dung r day