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Numerade Educator

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Problem 47 Medium Difficulty

Find an equation for the surface consisting of all points that are equidistant from the point $ (-1, 0, 0) $ and the plane $ x = 1 $. Identify the surface.

Answer

$-4 x=y^{2}+z^{2},$ paraboloid

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Video Transcript

in the given problem we have to find the question of set of points Which is a quick distance from this plane x equals to one and another. There is a point that is -10 little to have executes want all the wise it will be for the let the point B here X. Y. Is that? So the minimum distance from this point will be this one in this case at all points only that will matter because why? That must be saved for the minimum. So this line is minimum else any other line will be of greater land. So we will consider only this land has divan and these distances the two. Now we have to prepare these two presents. So the one can be simply written us x minus one and there's winds that will be same. So obviously those will be zero. The two can be retainers. It's the last one always squared plus here Y and Z. The friends also be considered. We are using pythagoras theorem. Does that square Now even he calls to Ditto which means X -1 will be equal to Over X-plus one square weiss parents. That is we just square on the border sides. And just a quick question expect less one minus two. X. This will be called X square plus one plus of poets. Less widespread as they described. So, these terms will you can cancel out mm from both the sides. So yeah, we can but I did know an education as y squared plus b squared question minus of forex. So this is the final form. A big question, mm. If you have studied treaties elementary, you can know that this is the form of electric parable Lloyd. The ship will be yeah. Mhm. Elliptic, yeah, bottom below it.