Find a standard form Cartesian equation for an ellipse with given properties

by RoRi

May 31, 2016

Find a Cartesian equation in standard form for the ellipse with center at $(-3,4)$ , semi-axes of lengths 4 and 3, and major axis parallel to the $x$ -axis.

Since the major axis has length 4 and is parallel to the $x$ -axis we have $a = 4$ , and since the minor axis has length 3 we have $b = 3$ . Since the center is at $(-3,4)$ we then have the Cartesian equation

$\frac{(x+3)^2}{16} + \frac{(y-4)^2}{9} = 1.$

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2 comments

May 17, 2023 at 6:46 am

William C says:

I believe the length of the length of the two axis would be equal to 2b and 2a respectively, not just a and b, but someone let me know if I’m wrong

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- June 14, 2023 at 1:52 am
  
  S says:
  
  You are right, that’s why exercise 13.24.10 has the solution given in the book. a and b alone are semiaxes.
  
  Reply

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