Question

Ma poate ajuta cineva la ex 12 cu oricare dintre puncte?

Answer 1

12.

$d:3x-4y+12=0$

$d:4y=3x+12$

$d:y=\frac{3}{4} *x + 3$
A(-2,3)

a)

$1) m_1=? \ d || d_1 \\</p><p>d: y= \frac{3}{4} *x + 3 \\</p><p>d_1: y=mx+n \\</p><p>d || d_1 ==> m_1=\frac{3}{4} \\</p><p>2) m_2=? \ d\perp d_2 \\</p><p>d: y= \frac{3}{4} *x + 3 \\</p><p>d_2: y=mx+n \\</p><p>d\perp d_2==> m_2*\frac{3}{4} = -1 \\</p><p>m_2= \frac{-4}{3}$

b)

$1)d: y= \frac{3}{4} *x + 3 \\ d_1: y=mx+n \\ d || d_1 ==> m_1=\frac{3}{4} \\</p><p>d_1:y=\frac{3}{4}*3+n \\</p><p> A(-2,3)\in d_1 \rightarrow 3=\frac{3}{4} *(-2)+n \\</p><p>3=\frac{-3}{2} +n \\ n= 3+\frac{3}{2} \\ n=\frac{9}{2} \\ d_1:y= \frac{3}{4}*x +\frac{9}{2} \\ d_1: 3x-4y+18=0$

$2)d: y= \frac{3}{4} *x + 3 \\ d_2: y=mx+n \\ d\perp d_2==> m_2*\frac{3}{4} = -1 \\ m_2= \frac{-4}{3} \\ d_2:y=\frac{-4}{3}*x+n \\ A(-2,3)\in d_2 \rightarrow 3=\frac{-4}{3} *(-2)+n \\ 3= \frac{8}{3} +n \\ n= 3-\frac{8}{3} \\ n= \frac{1}{3} \\ d_2:y= \frac{-4}{3}*x+\frac{1}{3} \\ d_2:4x+3y-1=0$