tentukan persamaan garis singgung parabola (y+3)²= 4(x-2) yang sejajar garis 2x+y-5=0

jawab

m garis  2x + y - 5= 0
m = - 2

y' = 0
2(y+3)y' = 4
y' = 4/(2y+ 6)
y' = -2

4/(2y + 6) = - 2
4 = - 2(2y + 6)
4 = - 4y -12
4y = -16
y = - 4  subke (y+3)² = 4(x - 2)
(-4+3)²= 4( x- 2)
1 = 4x - 8
4x = 9
x = 9/4

y - y1 = m(x - x1)
y - (-4) = -2(x  -9/4)
y + 4 = -2x + 9/2
2y + 8 = - 4x + 9
4x + 2y - 1= 0

Misal :
Pers garis singgung :
y = mx + c

2x + y - 5 = 0
m1 = -a/b = -2

sejajar : m = m1 = -2

y = -2x + c
substitusi kab ke (y + 3)² =4(x - 2)

(-2x + c)² = 4x - 2
4x² - 4cx -4x + c² + 2 = 0
4x² - (4 + 4c)x + (c² + 2) = 0
2x² - (2 + 2c)x + (c² + 2)/2 = 0

Menyinggung : D = 0

D = 0
b² - 4ac = 0
(2 + 2c)² - 4.2.(c² + 2)/2 = 0
(2 + 2c)² - 4c² - 8 = 0
8c - 4 = 0
c = 1/2

Persamaan garis singgung
y = mx + c
y = -2x + 1/2
2y = -4x + 1
4x + 2y - 1 = 0