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A(1, 3)
B (7, -3)
P=30
rownanie prostej AB
mAB=(-3-3)/(7-1)=-1
rownanie peku prostych
y-y1=m(h-x1)
y-3=-1(x-1)
y=-x+4 patrz zalacznik
Srodek AB
S(4,0)
Rownanie prostej prostopadlej do AB
m=-1/mAB=1
y-0=1(x-4)
y=x-4
|AB|=√(6²+6²)=6√2
C(x1,y1)∈y=x-4→
y1=x1-4
|SC|=√(x1-4)²+y1²
POLE P=1/2|AB|*|SC|
30=1/2*6√2*√[(x1-4)²+y1²]
10=√2*√[(x1-4)²+y1²] podnosze do kw
100=2(x1²-8x1+16+y1²)
x1²-8x1+y1²=34 i y1=x1-4
x1²-8x1+x1²-8x1+16=34
2x1²-16x1-18=0
x1²-8x1-9=0
Δ=64+36=100 √Δ=10
x11=(8-10)/2=-1 y11=-5
x12=(8+10)/2=9 y12=5
C(-1,5) lub C(9,5)
Pozdrawiam
Hans