1 vote
143 views

### How to simplify an equation corresponding to an ellipsoid? [duplicate]

The equation 29/36 - x/2 + x^2/4 + y/9 + y^2/36 - (4 z)/9 + z^2/9 == 1 is equivalent to ...
221 views

### How can I transform a quadratic into an factored equation? [duplicate]

How can I transform a quadratic polynomial in x and y into an equation of the form $(x-a)^2+(y-b)^2=c$? f = -9 x + (3 x^2)/4 + (3 y^2)/4; Completing the Square <...
85 views

I have a general query about simplifying expressions in Mathematica, which I will illustrate using quadratics. If I tell Mathematica to simplify $a x^2 + b x + c$ then ...
8k views

### Defining a function that completes the square given a quadratic polynomial expression

How can I write a function that would complete the square in a quadratic polynomial expression such that, for example, CompleteTheSquare[5 x^2 + 27 x - 5, x] ...
482 views

### Does Mathematica have a command that can directly get the center coordinates $(x,y)$ and radius $r$ of a circle?

I have an equation of a circle: x^2+y^2+2x-15==0 Does Mathematica have a command that can directly get the center coordinates $(x,y)$ and radius $r$?
786 views

### How can I get the center and radius of this circle?

I am able to make Mathematica plot the solution to a complex inequality as the interior or exterior of a circle : Let $a$ be a positive real constant, and $f(z) = \frac{z+1}{z-1}$. I want to get the ...
802 views

### Factoring the square of this polynomial?

I have a polynomial $$\frac{b^4}{a^4}-\frac{2 b^2}{a^2}+1$$ and I want to complete the square to get this kind of expression: $$\left(1-\frac{b^2}{a^2}\right)^2.$$ I had try: ...
147 views

### How can I transform the circle $x^2+y^2+a x+b y+c=0$ into $(x-A)^2+(y-B)^2+C=0$

I want Mathematica to put the circle given by $x^2+y^2+a x+b y+c=0$ into the standard form $(x-A)^2+(y-B)^2+C=0$, but I haven't been able to. I tried: ...
96 views

### SchurDecomposition doesn't work (in a weird way)

I have written a function to get the canonical form of a 3D quadric surface. This involves finding a unitary transformation of the coordinates which eliminates the cross-terms such as $xy$ or $xz$. ...