H = 4x and x= 3t write h in terms of t

Step-by-step explanation:

Standard equation of the parabola y2 = -4ax:

Parametric coordinates of the parabola y2 = -4ax are (-at2, 2at).

Parametric equations of the parabola y2 = -4ax are x = -at2, y = 2at.

Standard equation of the parabola x2 = 4ay:

Parametric coordinates of the parabola x2 = 4ay are (2at, at2).

Parametric equations of the parabola x2 = 4ay are x = 2at, y = at2.

Standard equation of the parabola x2 = -4ay:

Parametric coordinates of the parabola x2 = -4ay are (2at, -at2).

Parametric equations of the parabola x2 = -4ay are x = 2at, y = -at2.

Standard equation of the parabola (y - k)2 = 4a(x - h):

The parametric equations of the parabola (y - k)2 = 4a(x - h) are x = h + at2 and y = k + 2at.

Solved examples to find the parametric equations of a parabola:

1. Write the parametric equations of the parabola y2 = 12x.

Solution:

The given equation y2 = 12x is of the form of y2 = 4ax. On comparing the equation y2 = 12x with the equation y2 = 4ax we get, 4a = 12 ⇒ a = 3.

Therefore, the parametric equations of the given parabola are x = 3t2 and y = 6t.

2. Write the parametric equations of the parabola x2 = 8y.

Solution:

The given equation x2 = 8y is of the form of x2 = 4ay. On comparing the equation x2 = 8y with the equation x2 = 4ay we get, 4a = 8 ⇒ a = 2.

Therefore, the parametric equations of the given parabola are x = 4t and y = 2t2.

3. Write the parametric equations of the parabola (y - 2)2 = 8(x - 2).

Solution:

The given equation (y - 2)2 = 8(x - 2) is of the form of (y - k)2 = 4a(x - h). On comparing the equation (y - 2)2 = 8(x - 2) with the equation (y - k)2 = 4a(x - h) we get, 4a = 8 ⇒ a = 2 , h = 2 and k = 2.

Therefore, the parametric equations of the given parabola are x = 2t2 + 2 and y = 4t + 2.

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x

no solution

step-by-step explanation:

there is not enough information in the problem to solve.