Unformatted text preview: o a2 = 9.
All that remains is to ﬁnd b2 . To that end, we use the fact that c = 1 to get 424 Hooked on Conics
a2 − b2
9 − b2
9 − b2
12 = 2 1 = 9 − b2
b2 = 8
Substituting all of our ﬁndings into the equation
to be (x − 3)2 (y − 1)2
8 (x − h)2 (y − k )2
= 1, we get our ﬁnal answer
b2 As with circles and parabolas, an equation may be given which is an ellipse, but isn’t in the standard
form of Equation 7.4. In those cases, as with circles and parabolas before, we will need to massage
the given equation into the standard form.
To Write the Equation of an Ellipse in Standard Form
1. Group the same variables together on one side of the equation and position the constant on
the other side.
2. Complete the square in both variables as needed.
3. Divide both sides by the constant term so that the constant on the other side of the equation
Example 7.4.3. Graph x2 + 4y 2 − 2x + 24y + 33 = 0. Find the center, the lines which contain the
major and minor axes, the vertices, and the foci.
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