# HOW TO FIND EQUATION OF PARABOLA WITH VERTEX AND LATUS RECTUM

## About "How to find equation of parabola with vertex and latus rectum"

How to find equation of parabola with vertex and latus rectum :

Here we are going to see how to find the equation of the parabola if vertex and latus rectum is given.

Step 1 :

First we have to draw a rough diagram based on the given information.

• From the rough we can come to know the axis to which it is symmetric.
• From the rough diagram we can come to know the side on which it is open.

Step 2 :

Draw the perpendicular line from the vertex to the latus rectum, it passes through the focus.

Step 3 :

Now we have to find the distance between vertex and focus to get the value of a.

Example 1 :

Find the equation of the parabola whose vertex is (1, 2) and the equation of the latus rectum is x = 3.

Solution :

From the given information the parabola is symmetric about x -axis. To know about the side on which it is open we have to sketch a rough diagram.

From the rough diagram we come to know the parabola is open right ward.

(y - k)² = 4a (x - h)

Here (h, k) ==> (1, 2)

(y - 2)² = 4a (x - 1)

Distance between vertex and focus = a

V (1, 2) and F (3, 2)

VF = √(1-3)² + (2-2)²

=  √4

a  = 2

(y - 1)² = 4(2) (x - 2)

(y - 1)² = 8 (x - 2)

Example 2 :

Find the equation of the parabola whose vertex is (1, 2) and the equation of the latus rectum is y = 5

Solution :

From the given information the parabola is symmetric about y -axis. To know the side on which it is open we have to sketch a rough diagram.

From the rough diagram we come to know the parabola is open upward.

(x - h)² = 4a (x - k)

Here (h, k) ==> (1, 2)

(x - 1)² = 4a (y - 2)

Distance between vertex and focus = a

V (1, 2) and F (1, 5)

VF = √(1-1)² + (2-5)²

=  √(-3)²

a  = 3

(x - 1)² = 4(3) (y - 2)

(x - 1)² = 12 (y - 2)

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