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.
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Problem for practice: