## 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.

Problem for practice:

1.         Find the focus, vertex, equation of directrix and length of latus rectum of the parabola x²=-9y.
2.    Find the focus, vertex, equation of directrix and lenth of the latus rectum of the parabola x²=-12y.

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