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.
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Problem for practice: