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] ...
• 413
846 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 ...
• 201
848 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: ...
• 165
503 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 $r$?
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169 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: ...
• 45
1 vote
157 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 ...
• 1,473
119 views

### How to optimize the code for deriving the standard equation of the Apollonian circle?

The distance from a moving point in the plane to (0,0) is lambda times the distance from (a, 0). And lambda is not equal to 1. Find the equation The standard equation form for a circle is: ...
• 4,852
244 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 <...
• 8,629
161 views

### How to transform elliptic equation and hyperbola equation into standard form?

The elliptic trajectory equation and hyperbola trajectory equation are generated according to the code, but the final form is not the standard form. How to generate the standard equation form? The ...
• 4,852
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 $xz$. ...
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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 ...