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Answer:
Step-by-step explanation:
The standard for for the equation of a parabola is
The focus is given as
The directrix is given by
- Comparing focus given as
to formula of focus
, we see that
and
- Comparing directrix given as
to formula of directrix
, we can write
We can use the two system of equations [ and
] to solve for
and
.
<em>Adding the two equations gives us:</em>
<em>Using this value of , we can find
by plugging this value in either equation. Let's put it in </em><em>Equation 1</em><em>. We have:</em>
Now, that we know ,
, and
, we can plug these values in the standard form equation to figure out the parabola's equation. Doing so and rearranging gives us:
This is the equation of the parabola with focus and directrix