## 827 Reputation

11 years, 207 days

## Using algebra and equating coefficients...

Long handed way of solving the problem

See https://en.wikipedia.org/wiki/Parabola

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A parabola can be written in terms of the distance from directrix=distance from focus

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Equate the coefficients of Parabola and Par1

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## My variant on a solution...

My variant on solving it.

@vv  why did you define two parabolas? I see it gives more different solutions.

Edit:- corrected cond to b^2-a c=0

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## Another approach. Shift and Truncate...

Just in the spirit of another way to find a tangent without differentiation,

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Translate the conic at point [x0,y0] to the origin

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Truncate the conic to 1st order. this gives the tangent line to this conic at the origin

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Translate the line to [x0,y0]. This gives the tangent line to the original conic

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## Is this what you want?I could not get th...

complex_log_plot.mw

Is this what you want?

I could not get the document to upload.

```NULL;

z := x + y*I;

Plts := seq(plot3d([Re(k*log(z)), Im(k*log(z))], x = -3 .. 3, y = -3 .. 3, labels = ["Re(z)", "Im(z)", " ln(z)"], size = [800, 800]), k = [1, 2, 4, 6]);

NULL;
Plts[1];
Plts[2];
Plts[3];
Plts[4];
plots:-display(Plts);
NULL;
```

## This is a workaround I use...

I came up with this earlier in the year. Don't know how well it works for you graphics.

At the time I was taking notes from you tube that were formated in Scientific Workplace.

Basically I put a fixed sized table into the document constrained to A4 width. It is not perfect

but can be useful.

## mtaylor doesn't seem to work for f(x,y)...

I was typing my answer while @Kitonum answered. I had to work around the i2(x,y)  as shown. Using Maple 2021.2

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 > mtaylor(i3_r, [x,y,z], 10);
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 > eval( (5), [x = 0, y = 0, z = 0]);
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## A potentially useful previous answer...

how to copy a plot into zoomed plot - MaplePrimes

Plot inside one more plot - MaplePrimes

## use the "is" command in Maple...

7 nines as in your question
is(257^(1/2) <= 79999999/10000000);
false

8 nines
is(257^(1/2) <= 799999999/10000000);
true

## Try this...

```restart;
test := proc(x) local a; a := x^2; end proc;
test(5);
25

test(N*M);
2  2
N  M

```

I presume this is what you are trying to achieve.

## This way....

This shows how to get the answer.

## Is this what you want?...

RMB on the plot and in the list of oprions at the bottom is export. Click and export as GIF. Then put the GIF file in powerpoint.

Powerpoint_GIF.pptx

## A workable method to check inside or ou...

I came across this approach a couple of years ago for testing if a point is inside or oudside a polyogon.

The theory is given here Topology, Winding Numbers and Signed Area | Algebraic Calculus One | Wild Egg - YouTube

Basically you need to setup a garunteed exterior point to test with. Then ckeck is the segment from thr exterior point to the point of interest crosses any edges of the polyogon. The crossing number can be -1, 0, 1.   Sum the crossing numbers for all edges. If 0 then the point is on the outside else non zero means the point is on inside. The can handle non convex polygons.

Q is a random exterior point . P is the point of interest to check whether inside or outside.

Polygon Vertices

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Points for checking

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## As follows...

You should read the help on taylor and % as I have used that too

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The pattern is a geometric series based on

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