A few questions:
03-29-2022, 05:55 PM
Post: #1
 LodSb Junior Member Posts: 1 Joined: Mar 2022
A few questions:
1) How would I solve a system of equations to find the intersecting points of a circle and a line? If I use the solve app, it only gives me the points for one intersection, of the two that there are. Any idea how I would do this?

2) Is there a way I can covert back and fourth between decimal and scientific notation? I have seen multiple apps, but I'm not sure which one is the best, or most up to date.

3) Is there a way to analyze graphs to get stuff like the focal point or directrix of a parabola?

4) Is there a way to get the Fcn option that is available in the Function app to also show up in the Advanced Graphing app?

5) Is there a guide online or here somewhere for what all of the options do? I'm a pretty new user to this calculator and would like to learn more about it.
01-12-2023, 10:12 PM (This post was last modified: 01-12-2023 10:27 PM by jte.)
Post: #2
 jte Member Posts: 192 Joined: Feb 2014
RE: A few questions:
(03-29-2022 05:55 PM)LodSb Wrote:  1) How would I solve a system of equations to find the intersecting points of a circle and a line? If I use the solve app, it only gives me the points for one intersection, of the two that there are. Any idea how I would do this?

Two of the built-in apps come to mind. With the Advanced Graphing app, this could be done by
1. entering “(X-2)^2+(Y-2)^2=5” and “2*X+Y=4” for V1 and V2 (in the Symbolic view) and then
2. going to the Plot view and selecting Trace / PoI / Intersections with V2 (assuming the trace cursor is on V1; the d-pad can be used to go between the two intersections); or, to see the values in a table:
3. go to the Numeric view and select Trace / PoI / Intersections of V1 and V2 . (The app only scans the current plot area, so you’ll want to first ensure both intersections are visible in the Plot view.)   ⋮ (breaking my reply in two as there seems to be a limit of 5 images per post)

Attached File(s) Thumbnail(s)   01-12-2023, 10:18 PM (This post was last modified: 01-12-2023 10:28 PM by jte.)
Post: #3
 jte Member Posts: 192 Joined: Feb 2014
RE: A few questions:

With the Geometry app, this could be done by
• going to the Plot view and selecting Cmds / Plot / Implicit and entering “(x-2)^2+(y-2)^2=5”, selecting Cmds / Plot / Implicit and entering “2x+y=4”, (to bring up the two curves)
• selecting Cmds / Point / Intersections, picking one curve & pressing Enter, picking the other curve & pressing Enter, (to add the intersection points)
• going to the CAS view and evaluating “GC”; “GC(1)” will give the first point and “GC(2)” will give the second.  The Symbolic view, after interacting with the Plot view: Attached File(s) Thumbnail(s)   01-13-2023, 01:59 PM
Post: #4
 Arno K Senior Member Posts: 468 Joined: Mar 2015
RE: A few questions:
What about simply using solve in cas:
solve([((x-2)^2+(y-2)^2) = 5,(2*x+y) = 4],[x,y])
which provides
[x = ((1/5)*(sqrt(21)+6)),y = ((-2/5)*(sqrt(21)+6)+4)],[x = ((1/5)*(-sqrt(21)+6)),y = ((-2/5)*(-sqrt(21)+6)+4)]
so both intersections.
Arno
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