Question

Calcule o comprimento da corda determinada pela reta x+ y - 7 = 0 na circunferência x^2. + y^2 - 6x - 4x + 9 = 0

Answer 1

x^2 + y^2 - 6x - 4Y + 9 = 0 ==> y= 7-x
x² + (7-x)² -6x -4(7-x) +9=0
x² + 49-14x+x² -6x -28+4x +9= 0
2x² -16x +30=0 ==> : (2)
x² - 8x +15 = 0
-b/c = 8/15 = 3+5/3*5 => x'=3....x"=5

y'= 7-x' = 7-3=4
y"=7-x" = 7-5=2

P ( 3, 4)
Q( 5, 2)
corda=√(3-5)²+(4-2)²=√(4)+(4)=√8 = 2√2 ✓