# Parametric Rectangular Equations & Focus CoordinatesWatch

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#1
The question: Eliminate the parameter and find the corresponding rectangular equation for the set of parametric equations
x = 3 - t^2
y = t + 2
and find the coordinates of the focus of the resulting curve.

*****

So far, I’ve got:
x = 3 - (y-2)^2 and that takes care of the elimination/rectangular equation part.

How do I go about the second part to find the coordinates of the focus? What would the equation of the curve be from the rectangular equation I’ve found?
0
1 month ago
#2
(Original post by Multifine)
The question: Eliminate the parameter and find the corresponding rectangular equation for the set of parametric equations
x = 3 - t^2
y = t + 2
and find the coordinates of the focus of the resulting curve.

*****

So far, I’ve got:
x = 3 - (y-2)^2 and that takes care of the elimination/rectangular equation part.

How do I go about the second part to find the coordinates of the focus? What would the equation of the curve be from the rectangular equation I’ve found?
The curve is a parabola (horizontal axis of symmetry) and its in "complete the square" form already, so the focus can be written down
https://www.varsitytutors.com/hotmat...-of-a-parabola
or you may have to derive based on what you've done/know?
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