**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

Add 1 on both sides

(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 :**

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

After having gone through the stuff given above, we hope that the students would have understood "How to find focus directrix and vertex of parabola".

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