Solve for the following. Type your answer using digits. A rectangle with a length ofx−4 and a width of 8 has a perimeter of 34.
2 answers:
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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