In this page parabola focus we are going to see examples of finding focus, latus rectum, vertices and directrix of a parabola.
Find the focus, latus rectum, equation of directrix and vertices of parabola y² = 16x.
Comparing y²=4ax we get
a = 16/4 =4
Focus = (a,0)= (4,0)
Equation of directrix is x=-a so here it is x=-4
Latus rectum = length of the latus rectum = 4a =16
For the four standard forms corresponding focus, directrix, vertex and length of the latus rectum is given below.
In this page parabola-focus, we have discussed how to find the focus,
equation of directrix, vertices and length of the latus rectum. We will discus how to find the above in little different form of the equation.
Find the focus, latus rectum, vertices and directrix of the parabola
Rewriting the given equation y²-2y= 4x-13
Bringing to the square form by adding 1 on both the sides
y²-2y+1 = 4x-13+1
(y-1)² = 4x-12
(y-1)² = 4(x-3)
So the new origin is X= x-3 and Y=y-1, that is (3,1)] we get the equation of the parabola as Y²=4X.
Now we can proceed as in the first example.
Here 4a = 4 so a =1.
Focus = (a,0)=
X=a and Y=0
which is x-3 = 1 and y-1 =0
So the focus is (4,1)
Vertex = (3,1)
Equation of the directrix is X=-a
Length of the latus rectum = 4
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