What is the length of latus rectum for (y + 3)^(2)= 12(x - 1)

12 units

Step-by-step explanation:

The lactus rectum for a parabola is equal to 4 times the length of the focus from the vertex. Therefore, we need to determine the focus by using the equation for a vertical parabola.

We can deduce that , , and . Therefore, the focus of the parabola is or .

Because the focus is , then it is 3 units away from the vertex , making the length of the latus rectum 3*4=12 units.

b

step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (3, - 5) ← 2 points on the line

m = = = - 3

with m = - 3 and (a, b) = (3, - 5), then

y - (- 5) = - 3(x - 3), that is

y + 5 = - 3(x - 3) → b

step-by-step explanation: