Find the 90th term of the arithmetic sequence, 8.9, 13.6, 18.3, 23, …
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The sketch of the parabola is attached below
We have the focus
The point
The directrix, c at
The steps to find the equation of the parabola are as follows
Step 1
Find the distance between the focus and the point P using Pythagoras. We have two coordinates;
and 
.
We need the vertical and horizontal distances to find the hypotenuse (the diagram is shown in the second diagram).
The distance between the focus and point P is given by
Step 2
Find the distance between the point P to the directrix
. It is a vertical distance between y and c, expressed as 
Step 3
The equation of parabola is then given as
=
⇒ substituting a, b and c
⇒Rearranging and making 
the subject gives
We have the focus
The point
The directrix, c at
The steps to find the equation of the parabola are as follows
Step 1
Find the distance between the focus and the point P using Pythagoras. We have two coordinates;
We need the vertical and horizontal distances to find the hypotenuse (the diagram is shown in the second diagram).
The distance between the focus and point P is given by
Step 2
Find the distance between the point P to the directrix
Step 3
The equation of parabola is then given as
G(x) = (25 - x)/5 First lets call g(x) by its other name - y
y = (25 - x)/5 Now switch the x and y
x = (25 - y)/5 Solve for y which is now the inverse - call this
5x = 25 - y
y = 25 - 5x this is the inverse so = 25 - 5x
y = (25 - x)/5 Now switch the x and y
x = (25 - y)/5 Solve for y which is now the inverse - call this
5x = 25 - y
y = 25 - 5x this is the inverse so