# HOW TO FIND FOCUS DIRECTRIX AND VERTEX OF PARABOLA

## About "How to find focus directrix and vertex of parabola"

How to find focus directrix and vertex of parabola :

Here we are going to see how to find focus, directrix and vertex of the parabola.

Example 1 :

Solve for the values of focus, directrix and vertex of each parabola below and put your answer in tabular form.

y = - 4 x²

Solution :

From the given equation, we come to know the given parabola is symmetric about y-axis and open downward.

y = - 4 x²

x²  = -(1/4) y

4a  =  1/4

a  = 1/16

Vertex :

V (0, 0)

Equation of directrix :

y  =  -a

y  =  -1/16

Focus :

F(0, -a) ==> F (0, -1/16)

Example 2 :

Solve for the values of focus, directrix and vertex of each parabola below and put your answer in tabular form.

x  =  16 y²

Solution :

From the given equation, we come to know the given parabola is symmetric about x-axis and right downward.

x  =  16 y²

y² = (1/16) x

4a  =  1/16

a  = (1/16)(1/4)  =  1/64

Vertex :

V (0, 0)

Equation of directrix :

x  =  a

x  =  1/64

Focus :

F(a, 0) ==> F (1/64, 0)

Example 3 :

Solve for the values of focus, directrix and vertex of each parabola below and put your answer in tabular form.

y = x² - 4 x + 3

Solution :

From the given equation, we come to know the given parabola is symmetric about y-axis

y  =  x² - 4 x + 3

y  =  x² - 2 x (2) + 2² - 2² + 3

y  =  (x - 2)² - 4 + 3

y  =  (x - 2)² - 1

(y + 1)  =  (x - 2)²

(x - 2)²  =  (y + 1)

4a = 1

a = 1/4

The parabola is open up ward.

Let X = x - 2 and Y = y + 1

Example 4 :

Solve for the values of focus, directrix and vertex of each parabola below and put your answer in tabular form.

x = 3y² + 12 y - 4

Solution :

From the given equation, we come to know the given parabola is symmetric about x-axis

x = 3y² + 12 y - 4

(x + 4) = 3[y² + 4 y]

(x + 4) = 3[y² + 2 y (2) + 2²- 2²]

x + 4 = 3 [(y + 2)² - 4]

x + 4 = 3 (y + 2)² - 12

x + 4 + 12 = 3 (y + 2)² - 12 + 12

x + 16 = 3 (y + 2)²

x + 16 = 3 (y + 2)²

(y + 2)² = (1/3) (x + 16)

4a = 1/3

a = 1/12

The parabola is open right ward.

Let X = x + 16 and Y = y + 2

x = X - 16 and y = Y - 2

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