Not to be confused with quadratic equations, a quadric or quadric surface (quadric hypersurface in higher dimensions), is a generalization of conic sections (ellipses, parabolas, and hyperbolas).
Questions tagged [quadrics]
236 questions
5
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Find equation of the cone through the coordinate axes and lines $\frac{x}{1}=\frac{y}{-2}=\frac{z}{3}$ and $\frac{x}{3}=\frac{y}{2}=\frac{z}{-1}$.
Find the equation to the cone which passes through the three coordinate axes and the lines
$$\frac{x}{1}=\frac{y}{-2}=\frac{z}{3}$$ and $$\frac{x}{3}=\frac{y}{2}=\frac{z}{-1}$$
Above is the question from by exercise book, I understand the…
Singh
- 2,108
2
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1 answer
How to convert the equation to a standard form (paraboloid)?
I am given the equation: $9x^2 + 4y^2 + z = 3$
The standard equation of a paraboloid parallel to z-axis is: $$\frac{z-z_0}{c} = \frac{(x-x_0)^2}{a^2} + \frac{(y-y_0)^2}{b^2}$$
I think the given equation should be a paraboloid due to the $z$…
Amai
- 89
2
votes
1 answer
Compute projected radii of a rotated elliptic paraboloid
I'm working of a set of datapoints known to be an elliptic paraboloid on which I best fit the general quadric
$$ax²+bxy+cy²+dx+ey+f=0$$
Then I work with what I call radii projected on x an y defined as:
$$R_x=-\frac{1}{2a}, R_y=-\frac{1}{2c}$$
Now I…
Julien M
- 121
2
votes
2 answers
Quadric represented in matrix form
I just want to make sure I understand this right.
In the book our teacher describes matrix representation of quadric as (sorry for the 3x3 matrix it should be 2x2)
$$[ 1\,\,\, x^T]\begin{bmatrix}
c & b^T \\
b & A \\
\end{bmatrix}\begin{bmatrix}
1…
Zuzana Mitterová
- 143
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vote
1 answer
Where is the parabolic paraboloid?
In theory, any quadric surface can, through a series of translations and linear transforms, be converted to $f(X)+g(Y)+h(Z)=C$, where $f(X)=X^2$ (except in the case of the imaginary ellipse, where $f(X)=-X^2$), $g(Y)$ and $h(Z)$ may be positive…
No Name
- 741
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Find an equation for the surface consisting of all points P = (x, y, z) whose distance to the z-axis is twice their distance from the plane z = −1.
Having a lot of trouble with this one, as I can't find similar questions online or in the Stewart Calculus book.
Any help would be greatly appreciated!
bingobongo
- 43