Find the equation and identify the quadric surface defined by the set of points equidistant from a given point and a given plane.

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Finding the Equation of a Quadric Surface from a Locus of Points

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Find the equation of the quadric surface with points \(P(x, y, z)\) that are equidistant from point \(Q(0, -1, 0)\) and plane of equation \(y = 1.\) Identify the surface.

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What you need first

Distance formula in three dimensions
Distance from a point to a coordinate plane
Expanding binomial squares
Identifying standard forms of quadric surfaces

What this problem tests

Tests the ability to translate geometric distance conditions into an algebraic equation and classify the resulting quadric surface.

This problem is typical in a multivariable calculus or 3D analytic geometry course when introducing quadric surfaces and loci.

Finding the Equation of a Quadric Surface from a Locus of Points

What you need first

What this problem tests

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