Question

The line $x+y=1$ intersecpts the elilipse $4x^2+y^2=4$ at the point $P$ and $Q$. Find the coordinates of the point $P$ and $Q$, find the length of the chord $PQ$.

Answer 1

$4x^2+y^2=4$

$4x^2+(1-x{)}^2=4$

$x=1,\frac{-3}{5}$

$y=0,8/5$

$\Rightarrow \sqrt{{\left(\frac{8}{8}\right)}^2+{\left(\frac{8}{5}\right)}^2}$

$x+y=1$

$y=-x+1$

$P(1,0)$

$Q(\frac{-3}{4},\frac{8}{5})$

$\Rightarrow \sqrt{2}\left(\frac{8}{5}\right)$