Wolfram Research

Function Repository Resource:

Intercepts

Source Notebook

Compute the intercepts of a function with the coordinate axes

Contributed by: Wolfram|Alpha Math Team

ResourceFunction["Intercepts"][expr,{x,y}]

finds the intercepts of the expression expr with respect to axes variables x and y.

ResourceFunction["Intercepts"][expr,{x,y},{t}]

finds the intercepts of the parametric graph of expr with respect to axes variables x and y and the independent parameter t.

Details and Options

The first argument expr can be function of just one of the {x, y}, an equation (having head Equal) or a logical combination of equations.
Results of ResourceFunction["Intercepts"][expr,{x,y},] are returned in an analogous form to those of Solve: {{xsolx1,ysoly1,},}

Examples

Basic Examples

Find the intercepts of a line:

In[1]:=
ResourceFunction["Intercepts"][y == 3 x + 5, {x, y}]
Out[1]=
In[2]:=
Plot[3 x + 5, {x, -3, 3}, Epilog -> Join[{Red, PointSize@Large}, Point[{x, y}] /. # & /@ %]]
Out[2]=

Find the intercepts of a parabola:

In[3]:=
ResourceFunction["Intercepts"][x^2 + 2 x - 3, {x, y}]
Out[3]=
In[4]:=
Plot[x^2 + 2 x - 3, {x, -4, 2.5}, Epilog -> Join[{Red, PointSize@Large}, Point[{x, y}] /. # & /@ %]]
Out[4]=

Find the intercepts of an implicitly defined circle:

In[5]:=
ResourceFunction[
 "Intercepts"][(x - 1.75)^2 + (y - 0.3)^2 == 9, {x, y}]
Out[5]=
In[6]:=
Plot[{0.3 + Sqrt[9 - (x - 1.75)^2], 0.3 - Sqrt[9 - (x - 1.75)^2]}, {x, -5, 5}, Epilog -> Join[{Red, PointSize@Large}, Point[{x, y}] /. # & /@ %]]
Out[6]=

Find the intercepts of an parametrically defined ellipse:

In[7]:=
ResourceFunction["Intercepts"][
 x == 2 Cos[t] && y == Sin[t], {x, y}, {t}]
Out[7]=
In[8]:=
ParametricPlot[{2 Cos[t], Sin[t]}, {t, 0, 2 Pi}, Epilog -> Join[{Red, PointSize@Large}, Point[{x, y}] /. # & /@ %]]
Out[8]=

Scope

Intercepts[expr,] can handle the use of symbolic parameters in expr:

In[9]:=
ResourceFunction["Intercepts"][x^2 + a y^2 == 9, {x, y}]
Out[9]=

Resource History

See Also

License Information