数学 - Python - 放物線・だ円・双曲線 - 2次関数 - 2次曲線の平行移動と回転 - 2次曲線の平行移動 - 式の変形、概形の描画

学習環境

新装版数学読本3 (松坂和夫(著)、岩波書店)の第12章(放物線・だ円・双曲線 - 2次関数)、12.3(2次曲線の平行移動と回転)、2次曲線の平行移動の問24の解答を求めてみる。

1. $y^{2} + y = x$
  
  ${(y + \frac{1}{2})}^{2} - \frac{1}{4} = x$
2. $\frac{1}{2} y^{2} + 2 = x$
3. ${(x - 1)}^{2} + \frac{{(y + 1)}^{2}}{2} = 1$
5. $4 x^{2} - 24 x + 9 y^{2} = 0$
  
  $4 {(x - 3)}^{2} + 9 y^{2} = 36$
  
  $\frac{{(x - 3)}^{2}}{3^{2}} + \frac{y^{2}}{2^{2}} = 1$
6. $2 x^{2} - 4 x + y^{2} + 4 y = - 2$
  
  $2 {(x - 1)}^{2} + {(y + 2)}^{2} = 4$
  
  $\frac{{(x - 1)}^{2}}{2} + \frac{{(y + 2)}^{2}}{4} = 1$
7. $x^{2} - {(y - 2)}^{2} = 1$
8. $2 x^{2} - 4 x - (y^{2} + 4) = 0$
  
  $2 {(x - 2)}^{2} - {(y + 2)}^{2} = 4$
  
  $\frac{{(x - 2)}^{2}}{{(\sqrt{2})}^{2}} - \frac{{(y + 2)}^{2}}{2^{2}} = 1$

#!/usr/bin/env python3 from sympy import solve, plot from sympy.abc import x, y print('24.') eqs = [ y ** 2 + y - x, y ** 2 - 2 * x + 4, 2 * (x - 1) ** 2 + (y + 1) ** 2 - 2, (x + 3) ** 2 / 16 - (y - 1) ** 2 / 9 - 1, 4 * x ** 2 + 9 * y ** 2 - 24 * x, 2 * x ** 2 + y ** 2 - 4 * x + 4 * y + 2, x ** 2 - y ** 2 + 4 * y - 5, 2 * x ** 2 - y ** 2 - 4 * x - 4 * y ] for i, eq in enumerate(eqs, 1): ys = solve(eq, y) p = plot(*ys, (x, -10, 10), ylim=(-10, 10), legend=True, show=False) colors = ['red', 'green', 'blue', 'brown', 'orange', 'purple', 'pink', 'gray', 'skyblue', 'yellow'] for o, color in zip(p, colors): o.line_color = color p.save(f'sample24_{i}.png') p.show()