Locus
Another exclusive Foundation RISCWorld application
Exercise 6. Implicit Graphs
Sometimes formulae may not have 'y' neatly defined in terms of 'x' as in 'y=sin2x+4cos3x'. You may encounter expressions which have x's and y's mixed on the same side of the equals sign, for example 'x�-xy+y�=23'. This type of equation is called 'Implicit' and this exercise describes how Locus implements them.
The example given above is rather complicated, and is not the type of problem that would concern most people. However, simple implicit equations are often used at G.C.S.E. level. Consider the following problem:
- the following pair of simultaneous equations
3x + 5y = -1
2x - 3y = 12
This is the type of problem that Intermediate and Higher level G.C.S.E. students will be required to solve at some time, either graphically or algebraically. In fact, this is a pair of Implicit equations as the x's and y's are on the same side of the equals sign.
The reason simultaneous equations are written like this is to avoid the added algebraic complication of having fractional coefficients in the equation.
To examine the above set of equations first turn the grid on by ensuring that the 'Grid' option in the Settings window is ticked. Now set an appropriate domain and plot the first graph with auto-scaling switched on. Then turn auto-scaling off and type in the formula for the other equation. You will then be able to use Zoom to determine where the lines cross.
The Implicit routines are not yet complete, but they are adequate for plotting one to one, one to two and two to one mappings. However Locus may become confused if asked to do anything more complex. The reason for including this incomplete facility in the first release is that it is very useful for teaching linear simultaneous equations.
Foundation RISCWorld