Question

Y-x+5=0 dan x^2 + y^2 +2xy= 9 tentukan koordinat titik potong antara garis dan kurva .?

Answer 1

Verified answer

Jawab
y - x + 5 = 0 → y = x - 5

x² + y² + 2xy = 9
x² + (x-5)² + 2x(x-5) = 9
x² + x² -10x + 25 + 2x² -10 = 9
4x² - 10 x + 15 -9 = 0
4x² -10x + 6 =0
2(2x² - 5x + 3) =0
2(2x + 1)(x - 3) =0
2x + 1 = 0  atau x- 3 =0
x = - 1/2  atau x = 3

titik potong (x,y)
x= - 1/2  → y = x - 5 → y = - 5 1/2
x = 3 → y = x - 5 → y = -2
titik potong ( -1/2 , - 5/12) , (3, -2)