Question

seja r: x + qy -1 =0 e s:px + 5y + 2= 0 duas restas perpendiculares entre si. então, é correto afirmar quea) p/q = -5 b) p/q = 5 c) p/q = 1 d) p.q = -1 e) p.q = 5.

Answer 1

$\mathrm{r:x+qy-1=0\ \to\ qy=-x+1\ \to\ \boxed{\mathrm{y=-\dfrac{1}{q}x+\dfrac{1}{q}}}}\\\\ \mathrm{s:px+5y+2=0\ \to\ 5y=-px-2\ \to\ \boxed{\mathrm{y=-\dfrac{p}{5}x-\dfrac{2}{5}}}}\\\\\\ \mathrm{\Rightarrow Para\ r\perp s\ \to\ m_r.m_s=-1\ \to\ \bigg(\dfrac{-1}{q}\bigg)\bigg(\dfrac{-p}{5}\bigg)=-1}\\\\ \mathrm{\dfrac{p}{5q}=-1\ \to\ \mathrm{a)}\ \boxed{\mathbf{\dfrac{p}{q}=-5}}}$