m.n giai giup dum e cau nay nha(giai chi tiet dum e luon nha)

Question

Trong mặt phẳng Oxy, cho hai đường thẳng

$d_{1}: 3x+y+5=0 , d_{2}: 3x+y+1=0 và điểm I(1;2).$ Viết phương trình đường thẳng

$\Delta qua I và cắt d_{1},d_{2}$ lần lượt tại A và B sao cho AB=

$\frac{2}{\sqrt{2}}$ .

gio_lang_thang · Answer 1 · 1/7/2014 11:40:16 AM

pt dt

$\triangle co dang :y=ax+b hay ax-y+b=0$

Ta co :

$d_1//d_2 ,M(0;-5) \in d_1\Rightarrow d(d_1;d_2)=d(M;d_2)=\frac{4}{\sqrt{10}}$

$sin (d_1;\triangle )=\frac{d(d_1;d_2)}{AB}=\frac{2}{\sqrt{5}}\Rightarrow cos(d_1;\triangle )=\sqrt{1-(\frac{2}{\sqrt5})^2}=\frac{1}{\sqrt5}$

Mat khac :

$cos(d_1;\triangle )=\frac{|3a-1|}{\sqrt{a^2+1}\sqrt{3^2+1}}=\frac{1}{\sqrt5}\Leftrightarrow a=1$ hoac

$a=-1/7$

$\Rightarrow \triangle_1 :x-y+b_1=0;\triangle _2:(-1/7)x-y+b_2=0$

+)

$I(1:2)\in \triangle_1 \Rightarrow 1-2+b_1=0\Leftrightarrow b=1$

Vay ptdt

$\triangle_1: x-y+1=0$

+)

$I(1;2)\in \triangle _2\Rightarrow (-1/7)-2+b_2=0\Leftrightarrow b_2=15/7$

Vay ptdt

$\triangle _2: (-1/7)x-y+15/7=0$ hay

$x+7y-15=0$

1 Đáp án