## Focus question 7

In this page focus question 7 we are going to find out the focus, vertex, equation of directrix and length of the latus rectum of the equation

x²=-16y

Here the equation is in the standard form x²=4ay.The following table gives the necessary details of the standard and vertex form of parabola.

 Standard form Vertex form

 x² =4ay  If a is positive, then it opens up.  If a is negative, then it opens down. The focus is (0,a). The vertex is the origin (0,0)  The equation of the directrix is   y =-a The length of the latus rectum is   4a. (x-h)²=4a(y-k) If a  is positive, then it        opens up . If a is negative, then it opens down. The focus is (h, k+a)  The vertex is (h,k) The equation of the directrix is        y-k = -a The length of the latus rectum is 4a.

Solution:

The given equation is    x²=-16y.

Writing this equation in the standard form x²=4ay

x² = -4(16/4)x

which gives a = -4. Since a is negative, the parabola opens down.

Focus of the parabola = (0,a) = (0,-4)

Vertex                                = (0,0)

Equation of directrix    y= -a

y= 4

Length of latus rectum  = 4a = 4(4) =16.

Parents and teachers help the students to solve the problem in the above method in focus question 7 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.