# HOW TO FIND LENGTH OF LATUS RECTUM OF PARABOLA

## About "How to find length of latus rectum of parabola"

How to find length of latus rectum of parabola :

The formula to find the length of latus rectum is 4a. This is the general formula which is applicable for any parabola, like the parabola is open upward, downward, rightward, leftward if its center is (0, 0) or (h, k).

Let us see some example problems based on the above concept.

Example 1 :

Find the length of latus rectum of the following parabola

x² = -4y

Solution :

From the given data we come to know that the parabola is symmetric about y axis and it is open downward.

x² = -4y

x² = -4ay

4a = 4

Hence the length of latus rectum of the given parabola is 4 units.

Example 2 :

Find the length of latus rectum of the following parabola

y² − 8x + 6y + 9 = 0

Solution :

Now we have to convert the given equation into standard form.

y² + 6y = 8x - 9

y² + 2y(3) + 3 + 3² - 3² = 8x - 9

(y + 3)² - 9 = 8x - 9

(y + 3)² = 8x - 9 + 9

(y + 3)² = 8x

From this equation we come to know that the given parabola is symmetric about x axis and it is open right ward.

Length of latus rectum = 4a

4a = 8

Hence the length of latus rectum of the given parabola is 8 units.

Example 3 :

Find the length of latus rectum of the following parabola

x²− 2x + 8y + 17 = 0

Solution :

In order to find the value of "a",  we have to convert the given equation into standard form.

x²− 2x = -8y - 17

x²− 2x(1) + 1² - 1² = -8y - 17

(x - 1)² - 1 = -8y - 17

(x - 1)²  = -8y - 17 + 1

(x - 1)² = -8y - 16

(x - 1)² = -8(y + 2)

From this equation we come to know that the given parabola is symmetric about y axis and it is open upward.

Length of latus rectum = 4a

4a = 8

Hence the length of latus rectum of the given parabola is 8 units.

Example 4 :

Find the length of latus rectum of the following parabola

y = 2x²+ 3 x + 4

Solution :

In order to find the value of "a",  we have to convert the given equation into standard form.

[8(y - 4) + 9]/16  =  [x + (3/4)]²

(8y - 32 + 9)/16  =  [x + (3/4)]²

(8y - 23)/16  =  [x + (3/4)]²

[x + (3/4)]² = (8/16)[y - (23/8)]

[x + (3/4)]² = (1/2)[y - (23/8)]

From this equation we come to know that the given parabola is symmetric about y axis and it is open upward.

Length of latus rectum = 4a

4a = 1/2

Hence the length of latus rectum of the given parabola is 1/2 units.

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