## Parabola focus

In this page parabola focus we are going to see examples of finding focus, latus rectum, vertices and directrix of a parabola.

Example 1:

Find the focus, latus rectum, equation of directrix and vertices of parabola y² = 16x.

Solution:

Comparing y²=4ax we get

4a =16

a = 16/4 =4

Focus = (a,0)= (4,0)

Vertex= (0,0)

Equation of directrix is x=-a so here it is x=-4

Latus rectum = length of the latus rectum = 4a =16

For the four standard forms corresponding focus, directrix, vertex and length of the latus rectum is given below. In this page parabola-focus, we have discussed how to find the focus, equation of directrix, vertices and length of the latus rectum. We will discus how to find the above in little different form of the equation.

Example 2:

Find the focus, latus rectum, vertices and directrix of the parabola

y²-4x-2y+13=0

Solution:

Rewriting the given equation y²-2y= 4x-13

Bringing to the square form by adding 1 on both the sides

y²-2y+1 = 4x-13+1

(y-1)²  =  4x-12

(y-1)²  =  4(x-3)

So the new origin is X= x-3 and Y=y-1, that is (3,1)] we get the equation of the parabola as Y²=4X.

Now we can proceed as in the first example.

Here 4a = 4 so a =1.

Focus = (a,0)=

X=a and Y=0

which is x-3 = 1 and y-1 =0

So the focus is (4,1)

Vertex = (3,1)

Equation of the directrix is   X=-a

x-3 =-1

x=2

Length of the latus rectum = 4

Parents and teachers can guide the students to solve the examples on their own following the same method. Students can solve the problems given in the work sheets following the same method. If you have any doubt please contact us through mail we will help you to clear your doubt.

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