## 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.