I want to draw a picture of $(x-t)^2 + (y-t^2)^2 - t^2$ in $xy$ plane, with different values of $t$. I did it in a very silly way , namely,
ContourPlot[{
(x - 1)^2 + (y - 1)^2 == 1, (x - 2)^2 + (y - 4)^2 == 4,
(x - 3)^2 + (y - 9)^2 == 9, (x - 4)^2 + (y - 16)^2 == 16,
(x - 5)^2 + (y - 25)^2 == 25, (x - 6)^2 + (y - 36)^2 == 36,
(x - 7)^2 + (y - 49)^2 == 49, (x - 8)^2 + (y - 64)^2 == 64,
(x - 9)^2 + (y - 81)^2 == 81, (x - 10)^2 + (y - 100)^2 == 100,
(x + 1)^2 + (y - 1)^2 == 1, (x + 2)^2 + (y - 4)^2 == 4,
(x + 3)^2 + (y - 9)^2 == 9, (x + 4)^2 + (y - 16)^2 == 16,
(x + 5)^2 + (y - 25)^2 == 25, (x + 6)^2 + (y - 36)^2 == 36,
(x + 7)^2 + (y - 49)^2 == 49, (x + 8)^2 + (y - 64)^2 == 64,
(x + 9)^2 + (y - 81)^2 == 81, (x + 10)^2 + (y - 100)^2 == 100
},
{x, -110, 110}, {y, -110, 110}
]
I am sure there must be a simpler way. Could you give me a hand?
Answer
Use Table
to generate the values for different t
:
ContourPlot[Evaluate@Table[(x - t)^2 + (y - t^2)^2 == t^2,
{t, -20, 20, 1}], {x, -110, 110}, {y, -110, 110}]
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