Focus question 4

In this page focus question 4 we are going to find out the focus, vertex, equation of directrix and length of the latus rectum of the equation

y² +8x+2y+17=0.

Here the equation is in the standard form (y-k)²=4a(x-h).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        opens 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:

Here the equation y² +8x+2y+17=0 is in the quadratic equation form. Let us bring to the vertex form of equation.

y² +8x+2y+17=0.

y²+2y = -8x-17

y²+2y+1 = -8x-17+1(adding '1' on both sides)

(y+1) ² =   -8x-16

(y+1) ² =  -8(x+2)

This is of the form (y-k)²=4a(x-h) whose vertex is (h,k)

Here h=-2 and k=-1

and 4a = -8. So a = -8/4 =-2. Since a is negative the parabola opens up in the left hand side.

The focus is (h+a, k)  =  (-2-2,-1) = (-4,-1)

The vertex is (h,k)                    = (-2,-1)

The equation of the directrix is x+2 = +2

x=0

The length of the latus rectum is 4a =8

Parents and teachers help the students to solve the problem in the above method in focus question 4 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+4x-2y+3=0
2.    Find the focus, vertex, equation of directrix and lenth of the latus rectum of the parabola y²+4x+2y-3=0 