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define quadric equation

define quadric equation

Question Image
Grade:10

3 Answers

prafull
18 Points
6 years ago
test answer
prafull
18 Points
6 years ago
test answer
Sunil Kumar FP
askIITians Faculty 183 Points
6 years ago
In mathematics, a quadric, or quadric surface, is any D-dimensional hypersurface in (D + 1)-dimensional space defined as the locus of zeros of a quadratic polynomial. In coordinates x1, x2, ..., xD+1, the general quadric is defined by the algebraic equation
\sum_{i,j=1}^{D+1}xiQi,jxj +\sum_{i=1}^{D+1}Pixi +R=0
which may be compactly written in vector and matrix notation as:
xQx^{T}+Px^{T}+R=0
where x = (x1, x2, ..., xD+1) is a row vector, xT is the transpose of x (a column vector), Q is a (D + 1) × (D + 1) matrix and P is a (D + 1)-dimensional row vector and R a scalar constant.

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