Focus question 1

In this page focus question 1 we are going to find out the focus, vertex, equation of directrix and length of the latus rectum of the equation y²= 12x

Here the equation is in the standard form y²=4ax.The following table gives the necessary details of the standard and vertex form of parabola.

 Standard form Vertex form

 y² =4ax (y-k)²=4a(x-h) If a is positive, then it opens in the right hand side. If a  is positive, then it open in the right hand side. If a is negative, then it opens in the left hand side. If a is negative, then it opens in the left hand side. The focus is (a,0). The focus is (h+a, k) The vertex is the origin (0,0) The vertex is (h,k) The equation of the directrix is  x=-a The equation of the directrix is x-h=-a The length of the latus rectum is 4a. The length of the latus rectum is 4a.

Solution:

The given equation is    y² = 12x.

Writing this equation in the standard form y²=4ax

y² = 4(3)x

which gives a = 3

Focus of the parabola = (a,0) = (3,0)

Vertex                                = (0,0)

Equation of directrix    x= -a

x = -3

Length of latus rectum  = 4a = 4(3) =12.

Parents and teachers help the students to solve the problem in the above method in focus question 1 and they can guide them to solve the following problem using the above method.

The other three standard forms  and vertex forms of parabola are discussed in the focus worksheet.

If you have any doubt you can contact us through mail, we will help you to solve the problem.

Problem for practice:

1.         Find the focus, vertex, equation of directrix and length of latus rectum of the parabola y²=20x.
2.    Find the focus, vertex, equation of directrix and length of the latus rectum of the parabola y²=4x. 