title: plotting a curved line between 3 points with matplotlib
body: <p>I have 3 points on a scatter plot and want to plot a curved line connecting them. I'm currently using a line created with an ellipse equation and it has the general shape but there are 2 short straight lines on the left and right sides that can't figure out how to smooth out. Code and image below.</p>
  <p>Code:</p>
  <pre><code>import numpy as np
  import matplotlib.pyplot as plt
  
  ax = plt.gca()
  ax.set_xlim([-300,300])
  ax.set_ylim([-50,500])
  
  plt.scatter(-220,127.5)
  plt.scatter(220,127.5)
  plt.scatter(0,237.5)
  
  a = 220
  b = 110
  x0 = 0
  y0 = 127.5
  
  x = np.linspace(-a + x0, a + x0)
  y = b * np.sqrt(1 - ((x - x0) / a) ** 2) + y0
  plt.plot(x, y, c=&quot;black&quot;)
  
  plt.show()
  </code></pre>
  <p><a href="https://i.stack.imgur.com/4XDAU.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/4XDAU.png" alt="example of output" /></a></p>