## Focus question 3

In this page focus question 3 we are going to find out the focus, vertex, equation of directrix and length of the latus rectum of the equation

y² =-8x

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

Solution:

The given equation is    y² = -8x.

Writing this equation in the standard form y²=4ax

y² = 4(-2)x

which gives a = -2. So the parabola opens up in the left.

Focus of the parabola = (a,0) = (-2,0)

Vertex                                = (0,0)

Equation of directrix    x= -(-2)

x = 2

Length of latus rectum  = 4a = 4(2) =8.

Parents and teachers help the students to solve the problem in the above method in focus question 3 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. 