Parabolas do have a focus point Parabolas do have a focus point
Example:
Find the focus point on the parabola:
y = 2X2
There are two steps to the process. The first is to move the
coefficients to the Y The second step is to factor a 4 out of the Y
coefficient (who knows why a 4 works for this, but it does) What's
left as the Y coefficient is the distance
Step 1
Step 2:
So the distance from the bottom of the &quot;U&quot; of the parabola to
the focus point is 1/8 unit.
Let's try another... Example: Find the focus point of the equation:
Y = 8(X - 3)2 + 2
Step 1: Move the 8 away from the X
2
term
Step 2: Factor the mysterious 4 out of the Y coefficient
The distance from the bottom of the &quot;U&quot; (called the vertex) to
the focus point is 1/32.
Draw a line below the vertex of the parabola
the same distance as the distance to the focus.
Here's the deal. From any point on the parabola, it's the same
distance to the focus point as it is to the closest point on the line
we just drew ...
If the X2 term has a minus sign in front of it, the &quot;U&quot; is upside
down. That would make the focus point below the parabola vertex
and the horizontal line above it ...
But everything would still work the same. We could even reverse
the X and Y.
Example:
Find the focus point of:
X = 2Y2
Since this one is &quot;sideways,&quot; move the coefficient To the X term
and factor out the magic 4.
So the focus point is 1/8 unit to the right of the vertex of the &quot;U&quot;
And the line is 1/8 unit to the left of the vertex of the &quot;U.&quot;
THE DIRECTRIX