Question

Hi mates can u answer this????
Answer 1 and 2 both. Please......

Answer 1

Answer:
1) Put $y=0$ to get $X$ intercept.
Hence, $4x=12$ and $x=3$.
Put X=0 to get y intercept.
Hence: $12=-3y$; $y=-4$.
Thus sum of the squares is $16+9=\textcolor{red}{25}.$

2) The midpoint of the segment is $(2p, 2q)$.
Let the intercepts of the required line be $(a,0)$ and $(0,b)$.
Hence by midpoint formula, we have
$2p=\frac{a}{2}\\ \implies a=4p.\\ \mathrm{Similarly, \: we \: get \:} b=4q.$
Now using two point form of equation, we have:
$y-0=\frac{4q}{-4p}(x-4p)\\ \implies y=\frac{-q}{p}(x-4p)\\ \implies py=-qx+4pq\\ \mathrm{Thus \:} \\ \textcolor{red}{qx+py=4pq}$