(easy algebra 2, 20 points! )

write an equation of the parabola with vertex at the origin and the given focus or directrix.

1. focus at (3,0)
2. focus at (0,-5)
3. directrix y=2
4. directrix x=-4

solve each equation using perfect square trinomials.
1. 9x^2+12x+4=64

-2

7 - 9 = -2

reversed:

-2 + 9 = 7

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form

x=-7

step-by-step explanation:

x+3=-10

-10+3=-7

x=-7